I've now seen multiple cases (see comments) where checkpoint could have been parallelised much more aggressively.

The current default number of checkpoint threads is four. In the cases where I've seen slow checkpoints, it has always been the case that the CPU is underutilised, with all four checkpoint threads simply waiting on reconciliation, which is doing IO.

So as a thought experiment, what would happen if we gave it 1000 threads?

That number might be ridiculous, but I'm sure there's a point between 4 and 1000 that works better for most core counts out there. The key thing here is to understand the behaviour when there are too many threads, and trade that off against the current case of there not being enough threads.