If mining goes to PoS the cost tends to zero.
If the cost to secure the network tends to zero, then the cost to attack the network tends to zero is well.
The is the essence of the "nothing-at-stake" problem with PoS that, despite claims to the contrary, remains unsolved (and IMO very likely unsolvable).
Coins are a stake. Coins are not nothing when they have purchasing power. Is your concern that it is too easy to dominate purchasing power for a small currency? That makes sense when the market cap is low, but if you boostrap with PoW, to achieve market cap which is indefeasible in practice, then the problem is solved, is it not?