> Considering that TLC is exercising a very, very coarse model and a fuzzer is usually exercising a real interface/implementation. The former is dealing with an idealized simplification and the latter is dealing with a shape of real domain coverage when searching for counter-examples.

TLC checks the TLA+ specification, however detailed it is. In practice, it's true that it is usually much more useful to specify at a level well above the code, but it could be at the same abstraction level as the code (the specification could even be mechanically generated from the code), or even, in principle, much finer: you can refine the TLA+ specification to an arbitrary level, including down to the level of electronics in the CPU. However, very fine specifications are far less practical.

> Making even moderately complex TLA+ models or minor iterations on a simple model's depth of representation often results in exploding the search space for TLC and consequently the time to perform checking.

You can avoid the explosion by asking TLC to sample the behaviors in the same way a fuzzer does, but then you'll lose the exhaustiveness and the proof of absence of errors.