QC is not the problem (not now) but your estimate about "billions of years" is not correct. There are good reasons to avoid re-using bitcoin addresses:
Breaking ESDA is about prime factorization and not brute forcing sha2, hence it has nothing to do with ASICs used in bitcoin network. It is an active research field in mathematics and although it is hard to believe in discovery of a magical algorithm improvements are absolutely possible. Meanwhile Moore law is still working and attack costs are decreasing constantly.
This was just a comparison, if you consider having an equivalent power to the whole BTC network with ASIC dedicated to ECC (not SHA2) , breaking a single key would require several billions of years using the faster algorithm known today.
I agree with you, the most probable thing is that someone find the way to solve ECDLP in polynomial time and space, in that case, bitcoin would die immediately.
More importantly, it is not just about the algorithm itself, side channel/implementation dependent attacks are another serious class of threats.
In that case, your address is also not safe.
And we have conspiracy theories about NSA and its history of implanting back doors in its products.
Don't worry about that ! You can check the order of the curve, its embedding degree, primitive roots of unity, etc,... all is ok !
Finally, there is no reason to encourage disclosure of public keys and becoming exposed to various range of potential attacks specially when it comes to sensitive utxos which are supposed to stay live for long times and hold significant amounts of bitcoin.
There is also no reason today to discourage exposure of public key.