That said, I suspect that SpaceX is just trying to deal with the heat problem
This is kind of what I was thinking. That is, you’d be able to reuse your BFR many more times if the reentry speeds were significantly reduced. It would also give you some redundancy for reentry. Overall, I can see a lot of strengths to this concept.
So, I picture this:
BFR enters an atmosphere, deploys a very large inflatable heat shield to reduce most of the speed, then at a certain velocity that heat shield is ejected. After that, the normal heat shield does the rest of the slowdown, with most of the “damage” done to the inflatable heat shield, which may or may not be reusable.
It’s after seeing the graphs of temperature and deceleration that I really had this sense. It’s a similar deceleration rate, but at a much earlier point in reentry.
And if the balloon fails, you still have a super reusable heat shield.