I like the format of FIRST for a couple reasons:
1)It limits the pain to 6 weeks. For us coaches who have jobs and families that suffer from our time spent at FIRST, 6 weeks is about all we can do. (it can get very bad, coaches I've worked with have been threatened with divorce and actually stopped coaching)
2) Teams that have to ship their robot very early get hosed. Any local Atlanta teams can work up until the day of competition, whereas anyone who needs to ship their robot has to stop working weeks in advance in order to get their robot there.
3) It won't level the playing field. The best teams might have time to build two robots in parallel right now, but I'd bet some will build a second iteration of their first robot and be even more competitive than before. While smaller teams would be able to fine-tune their robot, the bigger teams would be proportionally further ahead because they're either more efficient, have more capabilities, or both.
If you want to work on something right until competition, join an SAE event
I have never worked for so hard for so long as I did doing Formula SAE. I say that as a veteran FIRSTer from a very small, yet successful, team.
Edit: I just wanted to add that our build budget is between $2k and $3k each year normally. One year it was $900 and we were finalists in the South Carolina regional.