A clear example of when this might be a good idea is DNS-over-HTTPS — you don't want the resolver being able to correlate multiple requests from the same client.
You _can_ try and do this with SOCKS5, however you need to be very careful to avoid sharing any state:
* You must use a new TCP connection for each request, with a new TLS and HTTP connection atop.
* You must ensure you do not use TLS Session Resumption or 0-RTT data.
* You must, to the maximum extent possible, be very conservative with what you send in the TLS ClientHello to avoid exposing fingerprinting data.
SOCKS5 is also unencrypted, and the request contains the destination: the hostname if the proxy resolves it, or the IP if the client resolved it itself (and ECH doesn't help here, since it only protects the SNI inside the TLS handshake that follows). With OHTTP, that's all inside the TLS connection to the relay.
OHTTP doesn't have the client sending up-front metadata about all the different encryption methods it supports to the gateway (it relies on the gateway to tell it what it supports, and the client just picks one); the gateway doesn't get to see any of the TLS fingerprinting surface (because that is only visible to the relay).
OHTTP also doesn't require there to be multiple new TCP connections made for every request (whereas with SOCKS5 you're looking at a new TCP connection from the client to the proxy, and from the proxy to the server, per request) — you can have a long-lived connection to the relay, and the relay can have a long-lived connection to the gateway (shared by many clients). That's a big latency win for applications like DNS-over-HTTPS.
The risks of key disclosure also differ between the two — with OHTTP, disclosure of the gateway key essentially means the relay can decrypt recorded traffic that used that key (as there is no forward secrecy), whereas disclosure of the client <-> relay and relay <-> gateway keys matters a lot less (because there is forward secrecy); with SOCKS5, you have forward secrecy via the end-to-end TLS connection.
For the use-case of a general-use proxy, work such as MASQUE provides a multi-hop approach to limit exposure to any single party, and that does provide an end-to-end TLS connection — but you with that you're back to exposing all the fingerprinting associated with it, though for a general use proxy you may also be sending session-specific data (like auth tokens) that clearly tie requests together anyway.