I think the bigger hole is DNS. Full-tunnel VPNs to primarily TLS-encrypted sites seems like overkill. Encrypted DNS plus an "HTTPS Everywhere" plugin should obfuscate enough info for most people without significantly affecting latency.
You still need the technical know-how to set up a DNSCrypt recursive resolver. The resolver then talks to the respective recursive chain in plain text as DNSCrypt is not something that is widely adopted.
I think that the SNI note below is probably the bigger hole.
Example: any traffic to 17.0.0.0/8 = user probably has an Apple device