Encryption everywhere isn’t about the individual content. By making it ubiquitous, it’s harder for bad actors to separate the encrypted data they want from the one’s they don’t. If only special content is encrypted, then just the fact that it’s encrypted is a flag for them. It also makes it much harder to ban. It’s pretty much impossible to ban the algorithms in TLS at this point. Too much depends on it.
TLS already has algorithms hardened against QC. The effects of QC against encryption are greatly exaggerated, anyway. The number of qubits that would be needed to break encryption may be too large to ever be feasible.
Get IPv6 going and stuff like SNI becomes unnecessary.