It's not the appearing out of nowhere that is a problem, it's the vanishing into nowhere! TOS takes place only 10 years later and so there can't be some huge new alien threat that affects the power dynamic in the region regularly, and then just be gone without a mention!
Or, let me rephrase that. They could certainly do that, but it'll take me right out of the story. At least that's what the Xindi and Suliban (sp?) in Enterprise did for me personally. Your mileage may vary. At the very least, it'll be natural to wonder what the heck happened to those guys but you'll be guaranteed not to find out!
I'm not going to get too hung up on this though. I love the time frame. I have confidence in the team producing this show. I think it'll be a success. While I have a slight preference for a continuation, I do love the time frame they picked for the show. I've said it before, if it had to be a prequel and I got to choose the time frame, it would be this exact time!
Mr Awe