No, the "moving forward" thing is about exploring the human condition, not moving forward on the calendar. You can tell the most amazing stories with the original crew, and at least everybody knows them. They'll draw people to the cinemas. I love DS9 and the Dominion War, but nobody but DS9 fans would actually get stories set during that time, and with those characters. Wouldn't be too profitable, I suppose.
A "reboot", "prequel" (whatever you want to call it) is the way to go. Something new, fresh, modern and exciting.... something that won't be weighed down by all established Trek canon (which would undoubtedly happen if we went to the 25th century. There is no way you could tell a story that would appeal to Joe Sixpack and Trekkies at the same time if you had to take into consideration every little established fact of Trek).
I trust JJ. He knows what he's doing.