If modus ponens is a valid form of argument, then the proposition "If (p&(If p, then q)), then q" is true. But this does not mean modus ponens just is that proposition. In fact, modus ponens is not a proposition at all; it’s a rule.
Rules do two things: They entitle you to do certain things, and they bar you from doing other things. For instance, perhaps there’s a rule in the library which says you may not use a cell phone in Quiet Areas, but may use it in other areas. This rule entitles you to use your cell phone in any area which is not designated as "quiet," and bars you from using it in the other areas. Rules usually apply within certain domains; and usually, a rule is inapplicable in any domain other the domain to which it belongs. For instance, suppose I’m on an airplane and I turn my cell phone on. The stewardess asks me to turn it off. I cannot respond by claiming to be entitled to use my cell phone on the airplane just because I am not currently in one of the Quiet Areas.
If modus ponens is a rule, what does it entitle me to do or say? In a logical context, modus ponens simply entitles me to write "q" whenever I have already written "p" and "If p, then q." It does not matter, in a logical context, whether "p" or "If p, then q" are true or false. It also does not matter whether I know or even believe "p" or "If p, then q." Indeed, it might turn out that "p" and "If p, then q" are known by me to be wildly false. Even in such a case, as long as I have already written these propositions, modus ponens, as a rule of logic, entitles me to write q.
This "logical sense" of modus ponens is, perhaps, the one which most people have in mind when they talk about modus ponens. But I believe there is another, wider, sense of modus ponens; let us call it the epistemic sense of modus ponens. We can divide epistemic modus ponens into two parts: weak epistemic modus ponens, and strong epistemic modus ponens. According to weak epistemic modus ponens, I am entitled to write "q" as long as I already believe that "p" and "If p, then q" are true. According to strong epistemic modus ponens, I am entitled to write "q" as long as I already know that "p" and "If p, then q" are true.
Consider that when people explain the idea behind modus ponens, they usually say something like: "If p is true, and "If p, then q" is true, then q must also be true." This fact does indeed explain what motivates the adoption of a rule like modus ponens, but it is important to note that the truth of "If (p&(If p, then q)), then q" probably never, on its own, entitles me to write "q." For if I have not already written "p" or "If p, then q," it does not matter what else happens to be the case; I am not logically entitled to write "q." Likewise, if I do not believe "p" or "If p, then q," I am not "weak epistemically" entitled to write "q"; and if do not know "p" or "If p, then q," I am not "strong epistemically" entitled to write "q." Indeed, there probably isn’t any meaningful rule which is justified solely by the truth of "If (p&(If p, then q)), then q." For "If (p&(If p, then q)), then q" is always true; yet there is no meaningful rule according to which I am always entitled to write "q."
Which of these senses of modus ponens is the primary one? I am not sure whether the answer to this question matters very much. It probably doesn’t matter, either, whether you think that one of these "senses of modus ponens" does not properly deserve the name "modus ponens" at all; the important thing is that the three senses are distinguishable and have been given different names.
Now consider two "closure principles." According to what I’ll call "entitlement closure," if one knows "p," and knows "If p, then q," then one is in a position to be entitled to believe q. According what I’ll call "knowledge closure," if one knows "p," and knows "If p, then q," then one is in a position to know q. (The "in a position to" clause just functions to ensure that these forms of closure don’t fail for uninteresting reasons.) In this post, I will try to show that to deny entitlement closure would be very bad. In a future post, I will argue that to deny knowledge closure might not be so bad; as things stand now, in fact, I think that knowledge closure probably does fail.
Straightforwardly, if entitlement closure fails, then strong epistemic modus ponens would not "work." Indeed, the negation of entitlement closure is really just a statement of the conditions under which strong epistemic modus ponens would be an bad rule. Similarly, weak epistemic modus ponens would not "work" either, since knowledge entails belief.
These facts alone might not show that entitlement closure has to be upheld. Certainly, if your view implies that modus ponens is a bad rule, then your view has extremely counterintuitive consequences. But if you think that the epistemic senses of modus ponens which I have suggested are not "really" representative of modus ponens, then denying entitlement closure does not entail that modus ponens is a bad rule. So a view on which entitlement closure fails does not, at least not yet, entail that modus ponens is a bad rule.
Let’s consider the logical sense of modus ponens. If neither of the two epistemic senses of modus ponens are the "real" modus ponens, then, I suppose, the logical sense of modus ponens must be the real one. According to the logical sense of modus ponens, as long as you have already written "p" and "If p, then q," then you are entitled to write "q." But why should you be entitled to write "q" under these circumstances? Perhaps it is simply because, if "p&(If p, then q)" is true, then "q" must be true. But this, I think, cannot be the whole reason. I have merely written "p&(If p, then q)"; that does not mean it is true, nor does it mean q is true, and still less, I think, does it mean I am entitled to write q. I claim that the following is a non sequitur:
1. I have written "p&(If p, then q)"
2. If "p&(If p, then q)" is true, then q must be true
3. Therefore, I am entitled to write q
Something, I think, must come between 2 and 3 to make this a complete line of reasoning. What must come between?
When one wants to explain what is "right" about modus ponens in its logical sense, one typically says something like this: "Logically, modus ponens works whether the premises are true or not, and it works whether you believe the premises or not. But it works because if you did believe p, and you did believe p entails q, then you would (or should) believe q. Indeed, if you believe "p&(If p, then q)," then you really must believe q; if you were to deny q, then you couldn’t really believe both of the premises after all. But in logic, we are acting as though we believe everything which has already been written." This line of reasoning, I think, is very close to a formulation of weak epistemic modus ponens. I suggest, then, that weak epistemic modus ponens provides the rationale for the logical sense of modus ponens. If weak epistemic modus ponens didn’t "work," then one would be left without any compelling reason to think that modus ponens in its logical sense does "work." Logical modus ponens would become an arbitrary rule without any available justification.
You might, of course, think that logical modus ponens is just an "arbitrary rule without any available justification". But I think most people would want to avoid this consequence, if possible. You might also think that logical modus ponens has a justification other than the ones which have been considered thus far. So I have not proved that denying entitlement closure has very bad consequences. But perhaps I have given the outlines of an argument which could show this.
In this post, I have been extremely vague about what I have meant by "entitlement." I hope, however, that context has made my meaning something less than completely obscure. I have said that there are rules in various domains, and that these rules entitle one to do certain things. In the epistemic domain, I think, one is entitled or not entitled to believe various things, and one’s entitlement or lack of entitlement derives from whether one has "followed the rules" in arriving at one’s belief.
[UPDATE: Rereading this post, I notice a few confusions in my argument. In the next post on this topic, I’ll try to de-confuse myself.]
E.G. 
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