Disclaimer:
1) I know nothing about searches, all I'm saying it's just based on the material in this topic.

2) it's too hot here and my brain is crashing every two seconds...

Now we are forcing the user to remove what SMF cannot use to do a search, silently hide it would allow him to at least get a result.
Is it the result he was expecting? Well, considering the relevance of an "a" in a search the probability that it is are rather high I think. Additionally: if he wants to do the search he has to remove the "a" and he will get anyway only the result SMF will be able to provide him. Nothing more, nothing less.
Is that the result he was expecting? For sure will be the same result he will get with SMF silently dropping the single chars. I can imagine.
Instead, if he is enclosing the search string into double quotes SMF searches for it without tell anything to the user (so from his perspective it is searching for the entire string).
So, provided that: present or not the "a" doesn't make any difference. I'd expect that "present" or not it would return the same result (of course my experience here is basically null).
So, instead of saying "before being able to search anything you have to remove all the things SMF doesn't want (I know it's not that, but from the user perspective it is) to search", wouldn't be much friendlier to say: "We have searched without considering the "a" because anyway it would be meaningless search for such a piece of information"? (that AFAIR is what google was used to do a long time ago, but now has stopped)
It would be one less click and one less edit for the user searching something (an improvement I'd say), and the result will anyway be the same.
Am I completely off track?