PQC is obviously desirable for a privacy-centric messaging service but running one of shor's algorithms for breaking RSA and ECC is still a way away. for an n-bit RSA key, you'd need 3n qubits. RSA keys are 2048-4096 bits (hopefully the latter). the current largest circuit-based quantum computer is ~1200 qubits AFAIK. that is 10x less than you'd need to break a recommended size RSA key.
even then, as far as i can tell, current PQC is mostly a guess as to what quantum computers will not have algorithms in class BQP to break them.
if your threat model truly is nation states who are actively recording your communications with near-future access to that amount of error-corrected quantum compute then sure. but for someone more concerned with big companies invading their privacy, platforms without PQC do their job perfectly well (as long as their cryptosystem provides perfect forward secrecy, IND-CPA, IND-CCA1/2, though i'm not a cryptographer so don't quote me on that).