Runtime size depends on a few things. The biggest is JIT vs native. If you're willing to dedicate the time to making (or interfacing with) a completely native compiler, then the runtime penalty isn't that large. In contrast, any halfway decent JIT is going to be several MB of code (and unlike an image, has to be parsed and executed -- potentially on slow phones).
In both cases, the GC issue is non-trivial. LLVM has finally started to make performant GCs possible. Wasm (to my knowledge) doesn't have similar capabilities and guarantees (I suspect the are actually impossible with untrusted GC code). The only viable solution IMO is the addition of GC primitives and hope that your particular language maps well on that specific browser's GC.
But the web is only one aspect. Web apps are likely going to take over a huge part of client development.