A valid concern.
> which currently, effectively don't work.
Citation needed.
> HTTP 2 is for example slower than HTTP 1.1 over modern TLS even on near perfect connections.
H2 attempts to solve a number of problems present in HTTP 1.1 when your connection _isn't_ perfect -- head-of-line (HOL) blocking comes to mind, although since it still uses a single TCP connection, it's not a complete solution. It also provides header compression which can yield significant performance wins (bandwidth usage, latency if it reduces RTTs, CPU usage although this is always a mixed bag with compression).
H3 solves the transport-layer HOL blocking issue, and has a number of other RTT-reducing features (e.g. removing the need for TCP 3-way handshake -> TLS handshake -> actual sending of requests by mandating the use of TLS, which admittedly can have performance impacts compared to, say, unencrypted HTTP/1.1).
It does have a number of aspects which could negatively impact performance depending on your use case (e.g. userspace congestion control, always-on encryption).
If you're dealing with small resources without HTTP pipelining where individual HTTP requests can and will complete in 1 RTT (and parallelization is limited because of dependencies between resources, e.g. a HTTP page contains an iframe which contains a js file which fetches an image), then your end-user latency will be dominated by the number of RTTs imposed by the underlying transport.
And even if you include pipelining (assuming a non-buggy implementation, which inherently limits concurrency in order to reap its benefits), then you're still subject to HOL blocking, both request- and connection-level, which is problematic in moderate loss scenarios (wifi, mobile).