Do Americans leave the ordinal suffix out of dates?

The Chicago Manual of Style and Associated Press Stylebook both say to leave out the ordinals.

However, since the ordinal is nearly always pronounced when the date is read, I think this seems absurd. Searching around the internet has not revealed any reason to leave out the ordinal beside an appeal to these authorities. I have no idea why they think this is good style.

I write out the ordinals, and would encourage others to do so as well, style guides not withstanding.

America's a big place, and you're likely to find people that speak and write it differently. I'm an American and I've been known to write both "December 31" and "December 31st", or "31st of December", though usually "12/31" suffices. When I speak, I virtually always say the suffix... something like "December the thirty-first." I wouldn't be confused or surprised by seeing it any of these ways.

I mean, you might as well ask why French people eat parsnips. I assume some have and do, some haven't and don't, some aren't even aware of choices they've made in that regard and at the end of the day it doesn't really matter or characterize the French people in any meaningful way (do all non-American people always add the ordinal suffix? If no, why not, and why should the answer for Americans be any different?).