The Celtics ranked fifth in the league this year in eFG% against. (I can't find TS% against numbers, which I would prefer, but you work with what you've got.) They were a pretty average team at defending the 2, 19th in the league in 2P% against, but were excellent at shutting down threes, 2nd in 3P% against. So, I don't think lack of rim protection is a major concern if they continue to be a team that can successfully make it really hard to shoot threes. They could use some upgrading in the rebounding department, but I'd also posit that part of their rebounding struggles are linked to their being really really good at defending threes. In other words, being aggressive at getting out and contesting every shot leaves fewer guys in position to rebound on a regular basis.
I do not understand why people want to fundamentally restructure a roster format that has shown itself able to consistently outperform its talent level over the course of the last 2 years. The team just needs more talent, and that may or may not entail restructuring the nature and approach of the team. If a guy who plays like prime Dwight Howard becomes available to the Celtics, there is no way floor spacing concerns should impact our willingness to bring that player in. But, if what is available this offseason are upgrades to our wing talent (and that is what is available) there is no evidence of any flaw in the design of the current roster outside of a talent deficiency relative to the 2-4 best teams in the league.
All that's to say that there are a lot of people here who seem wedded to a particular type of roster structure, and that is foolish on all counts. What this team needs is more talent. If that talent is a rim-protecting big, great. If it is better scoring and shot-creation, that's great too. Upgrade the talent, not any particular skill. Thankfully, I'm pretty sure Ainge gets this even though many on this board appear not to (many others do get it--this is not a universal critique).