Even if English speakers recognized in some way that the "bank" in "Mountebank" had something to do with banks, they also likely would have to assign some meaning to the "Mounte" part, which they do not. This is pretty much a rare word anyhow, so typical speakers of English are likely to not have any transparent morphological composition for it.
Hmmm? They're the dudes who mount a bank (to sell stuff from it). Mount like getting on top of and bank like a river bank.
In this case I think it's actually supposed to be the "bench" meaning of "bank" (which as far as I know is obsolete in English, if it ever existed), and these two meanings are distantly related to each other (as well as the financial bank), but their meanings are so far from each other that English speakers don't really think of them as being the same.
"Bench" and "bank as in river bank" have the same distant origin, so I'm not sure if you're disagreeing with me and if so what about.
I am an English speaker and I personally have always thought "they mount a bank."
If you think they're mounting a river bank, that's fine, but that's still folk etymology since the borrowing from French / Italian is referring to a bench or raised platform, just like in the card artwork. The bench meaning of 'bank' is probably unavailable to English speakers at least currently -- the Oxford English Dictionary lists it as historical.
I don't think they're mounting a river bank, I think they're getting up on a little stage or something. But when I look at the word, I see "mount a bank," bank as in river bank, noting that that meaning of bank doesn't require the bank to be by a river.
I am still not sure what argument I'm supposed to be having, so I'm going to go back to the start, as is my wont. You said: "Even if English speakers recognized in some way that the "bank" in "Mountebank" had something to do with banks, they also likely would have to assign some meaning to the "Mounte" part, which they do not." English speakers, anecdotal evidence me, assign "mount" to the "mounte" part. You said they don't assign "mounte" meaning; I am a counterexample.
OK, I wasn't clear -- I meant that if speakers, including you, want to interpret the word "mountebank" as composed of more than one morpheme, then there are just two options in current English for the "bank" part: either the financial institution or the side of the river. So, either this term means to get up on top of a building where they perform transactions of money, or on top of the side of a river. Neither interpretation has anything to do with the word mountebank, so it is difficult to say that this word is really polymorphemic.
You may recognize parts of words within this word, but especially since you mention that you "note that that meaning of bank doesn't require the bank to be by a river", this seems like you really don't think this word is made up of the word "bank" at all.
Another example: 'dismantle' -- you might recognize the part of the word 'mantle', the thing above a fireplace, but actually this word has nothing to do with fireplaces. It just means to take anything apart. For most English speakers this word has just one morpheme. Originally, of course, this word meant "to take off a cloak", since there is this other meaning of the word mantle that refers to clothing, but this word history is entirely irrelevant to how current English speakers store this word in their mind.
