Both these and the oft-maligned gas core fission rocket[1] have a common problem: "what does a nuclear flame holder look like?"

Less problem with water of course, but you're also holding down the reaction area temperature, and reaction engines (regardless of whether the reaction is chemical or nuclear) generally reward high temperatures.

Unfortunately there are some other things that ALSO have opinions about temperature, like "all known physical materials".

[1] https://en.wikipedia.org/wiki/Gas_core_reactor_rocket#Heat_t...