True, if somewhat situationally. Remember what happened to the French at Agincourt...
There will always be exceptions. Point is I'd imagine it would be difficult to hold a longbow steady or reload a musket while being trampled by horses, lances, and whatever else. I say imagine, because I have yet to find myself in such a situation
The main problem with making melee units the undisputed focus of combat is that the AI will always be able to pump out more of them than the human player at high difficulty levels.
Which is fine. While many of us are comfortable playing at Immortal-ish range, it shouldn't be what the game is balanced around. At worst, the difficulties would have to be modified to have less carpet of doom, which I think would be a good thing.
People don't necessarily build them because they're too powerful; they build them because they're currently the only thing that works.
One of the things I play around with most when modding the game is giving the AI a passive combat bonus. It doesn't represent the changes I mentioned above exactly, but it is close enough to get a feel for how it plays out. It isn't until up to ~65% combat strength that it begins to feel too cheap--as in you do next to no damage with an archer and then get one-shot the next turn. Even then I could manage once I get a general and a few promotions.
My only point here is that 65% is quite significant, so there is quite a bit of room for boosting basic infantry before it begins to break the game. If archers are currently "the only thing that works" then that should be a clear indicator something needs to be looked at.