I haven't heard many arguments against dozens. In fact, there are some groups that specifically argue for duodecimal systems. I'd be interested to hear your position in more detail.
My main problem is that it's longer than "tens". And I have 10 fingers. And I use base-10 for everything, including counting the dozens. It's just more logical (and I say that without reading through the wiki page, so sorry if whatever I say doesn't make any sense with that in mind. I'm not good with words).
It's only logical because that's what overwhelmingly likely what you grew up using. There are duodecimal finger counting systems. (Counting to 12 isn't even all that impressive, considering counting each finger as a binary digit results in 1024.)
Also, "9 dozen" is the same in either base. "10 dozen" would become "ᘔ dozen", "11 dozen" to "3 dozen", and "12 dozen" to "10 dozen".
Finally, a dozen dozen is a gross and a dozen gross is a great gross, which at 1728 would be a likely replacement for "ton".
http://en.wikipedia.org/wiki/Duodecimal#Advocacy_and_.22doze...