TLB isn't "flushed" so much as it is useless across different memory address spaces. Switching processes means switching address spaces, which means you have to switch the contents of the TLB to the new process' TLB entries, which eventually indeed flushes the TLB, but that is only over time, not necessarily the moment you switch processes.

> Like processes, heavy-threads would have mostly-separate address spaces by default.

This thus conflicts with the need to not flush TLBs. You can't not change TLB contents across address spaces.