My Ford Escape came from the dealer with a class 3 trailer hitch (1.25") and towing package that included updgraded battery and a few other things. Don't know if Honda is charging for those upgrades as well. Probably not. Honda is a premium product and they charge premium prices to boot.
Having said that, and having an 1.25" receiver hitch on my truck...I'd vote for the 2". I think there's a whole lot more usefulness out of the 2" that you don't have with the (whimpy) 1.25". But, maybe it's a Freudian thing...