I enabled this at some point in time, it's amazing how many services I use that rely on Google. After I got over 20 application specific passwords, which I guess are tell alls, I decided it wasn't worth the complication. The real problem with this was apps implementations of the two-factor auth. I haven't looked at any of the APIs (I know they don't exist for some services like Reader) but if the entirety of the auth was only typing in a code sent to your phone I would've stuck with it. It's when you get into these application specific passwords, especially when you have to create new ones on your phone, that I think it's more trouble than it's worth.
I'm not sure I follow, what services you are talking about that rely on Google? I only had to generate a few ASPs for my email clients, and little more. I use most of the Google-provided apps on Android though, so I never have to actually log in to my Google account from my phone/tablet, it might be the case that on iOS the situation is different?
I'm sorry I said that strangely. The point I was trying to get across that you use Google logins a lot. For example I have 4 email accounts on 4 or 5 devices, in multiple mail applications along with service specific apps like the Google plus or similar apps. Which ends up with a lot of application specific passwords.