Since the new ownership and Ainge took over they have always run the team with the goal of winning championships. History shows overwhelmingly that you need at least one MVP-caliber, no doubt-about-it HOF player surrounded by all-star level talent to do so. They are still looking for that player.
Now, there's something called the salary cap that limits your ability to add players once you've exceeded it. If they fill up the cap with too many players who are good but not great, they will end up like the 01-02 Celtics teams or Toronto the last few years or countless other teams in history that were only good enough to be second best and had to blow up their team and start over. The Celtics operate in a way that, when they make their move they want to be sure they actually have a shot at a title. In 2008, it worked.
It's quite possible that the Cavs and the Warriors are simply too dominant right now that no possible moves in the next few years could challenge them. The Warriors took advantage of the salary cap suddenly skyrocketing to add Durant, that is not something that normally happens. The Cavs were incredibly fortunate to win multiple draft lotteries that allowed them to draft LeBron the first time, draft Irving, and trade for Love (also, Tristan Thompson was a 4th overall pick). They even got to waste a pick on Anthony Bennett. They were incredibly fortunate to be able to add that much talent and then sign LeBron as a FA (I think technically it was a sign-and-trade, but he would have gone there anyway).
The Celtics are going to continue to improve the team but they are not going to expend all their assets and sacrifice the future to make an impossible run at the Cavs and Warriors. It might be different if a player like Kawhi Leonard, Anthony Davis, or Giannis Antetokounmpo suddenly became available, but I think we all know that's not going to happen anytime soon.
Frankly, the names of the people that are FAs or whom might actually available are 2nd tier stars: Paul George, Jimmy Butler, Blake Griffin, Gordon Hayward, etc. They would improve our team but we wouldn't jump a level by adding them. What we would do is just solidify our standing as the best team of the 2nd-tier teams in the East.
The Celtics are smart. They're going to keep their draft picks. We already may have a future star in Fultz (think James Harden-level ability). Brown may not be a future All-Star but he's raised his floor to be a starter on a very good team. Sign Hayward and keep the kids, then figure it out.
Also, they need to be careful with how much they pay Thomas. Just because he can get the max elsewhere doesn't mean he's worth that. Sure, you could pay him just because you don't have anyone else but then you'd be making the mistake that bad teams make - overpaying their own flawed guys because there are no other options.
If the moves were out there to make up for Thomas' deficiencies so that we could still pay him and not have too flawed a team, then sure go ahead and go over the cap to sign him. I don't think the moves are out there though.