Further thoughts:
1) This isn't a problem that Feats can solve, for a number of reasons:
A) Feats aren't in all 5E games at all.
B) You don't get ANY Feats in 5E until level 4/5 (I forget), which is literally half the career of most PCs in my experience, and quite likely months of play. Also you may well have a magic weapon by then, so if a weapon is kind of dodgy until you get a Feat, it's probably just going to get ignored.
C) Even when you do FINALLY get your first Feat, you probably have 16-18 in your primary stat (and you are a weapon-fighter of some kind for this discussion, not a finger-wiggler), so you are comparing Feat #1 to +1 to hit and damage all the time on everything you do. Even dim players can usually go "Well to hell with that Feat..." to that. For less-optimized PCs, Feat #2 is likely to get eaten the same way, because even dim players can see "I need to get my main stat to 20, then I can forget about it"-type logic (in fact they are most likely to do that, in some ways).
So yeah, if you need to be level 8 or 12 (seriously these are the levels for Feat #2 and #3) before you get your weapon working "properly", then damn, I don't expect to see Feat-reliant weapons being very popular.
2) Most players don't charop, but most can spot a dud weapon, due to instinctive maths and so on. Only deceptive weapons often fool them (lots of D4s and the like). So duds will get ignored.
ACCORDING to Chambers's "Encyclopaedia," the quarter-staff was "formerly a favourite weapon with the English for hand-to-hand encounters." It was "a stout pole of heavy wood, about six and a half feet long, shod with iron at both ends. It was grasped in the middle by one hand, and the attack was made by giving it a rapid circular motion, which brought the loaded ends on the opponent at unexpected points."
Some more info from wikipedia Here:
http://en.wikipedia.org/wiki/Quarterstaff
Time to stop confusing a recognised weapon with a walking stick. Stylisticly a druids quaterstaff might not be ironbound but will be hardened and weighted on the end to make it as effective.
That you had to look this up shows that there is a problem here.
D&D will need to do a good job explaining what a quarterstaff is, because 99% of players, especially newer ones and people who aren't military history buffs, will indeed envision "a wizard's staff". The fact that wizards in D&D use them, and that there is no "staff" as separate weapon will reinforce this view.
Further, popular fantasy/quasi-fantasy like Robin Hood tends to show quarterstaffs as pretty much "big eff off walking sticks", not iron-bound weapons, so that's the only other likely image people have.
If D&D wants another perception, it is up to D&D to create that perception, and sneering at people who don't share it ("time to stop confusing...") is unhelpful, I would suggest, given their perception is not an unreasonable one for even a normal fantasy/medieval fan, let alone a normal member of the public.