There are actually two types of middlebox problems:
1. DNS resolvers which don't carry new record types. 2. Middleboxes which don't properly handle UDP-based protocols
(2) applies to both H3 and to TurboTLS, and in both cases you need some kind of fallback in case things fail.
(2) applies to TurboTLS as specified. However, it's worth noting that H3 also has a DNS-based mechanism for advertising support via the HTTPS record (that is also used for ECH). However, you can also advertise H3 support via Alt-Svc, so presumably you could do the same with TurboTLS.
In general, any new transport like H3 or TurboTLS has to be offered on a best-effort basis with a fallback, otherwise you'll have a lot of hard failures.
HTTP/3 is in most browsers under 3 years old, and most server stacks support it (usually with a bit of extra config).
Alt-Svc is an http header, by the time you get http you already have TLS setup. In a Alt-Svc workflow you generally advertise h2 in TLS ALPN, then use Alt-Svc to advertise h3 capability in the headers of the first response, and then the client establishes a h3 connection and closes the h2 connection when it is ready (and the h2 connection does not have any queued requests). At least that is my understanding.
(Well, technically ECH can obtain server configs any way, but HTTPS is recommended.)
With that said, the unusual performance dynamics of the Web make connection setup latency particularly important by contrast to, for instance, SMTP, where people don't really get bent out of shape if a message takes another 200ms to be delivered.