There are implications for business accounts too: if you need a real name you'll no longer be able to sign up in Adwords with something like admin@<company-domain> (and changing the company's Adwords to another person becomes a headache).
I can see why Google would want to clamp down on semi-anonymous gmail accounts. I'm sure many of us have used them for convenient purposes with no ill intent, myself included, but we all know that they are often used for spamming. Overall I'm OK with this as long as they don't remove the lesser-known feature of creating infinite aliases with a plus sign (myemail@gmail.com -> mymail+whatever@gmail.com). It doesn't work everywhere, and it doesn't solve all of the needs for using semi-anonymous emails, but it often solves a lot of them.
Still, I won't be surprised if demand starts rising for other free anonymous mail services. Google's UI presents a nice barrier to entry, though (of course, others exist but none are as popular right now).
That could be one way for anyone concerned with the integration to get around this. Create a fake name, Google will disable the G+ profile and you can still use Gmail.
I wanted to raise a similar concern for YouTube accounts. If you have to provide your Real Name to post to YouTube, a lot of people will self-censor, and some important or valuable videos may never get posted.
Please cite some evidence for this. I can't find any. The policies are still in place, and the last statement I can find from Google dates to October and says they'd be supporting pseudonyms in some vague form in a "future update".