You'd run it on any architecture that can spawn a process and attach to stdin/stdout.
The overhead of spawning a process is not the problem. The overhead if your runtime is huge and/or slow to start could be, in which case you simply wouldn't run it on a serverless system - which is ludicrously expensive at scale anyway (my dayjob is running a consultancy where the big money-earner is helping people cut their cloud costs, and moving them off serverless systems that are entirely wrong for them is often one of the big savings; it's cheap for tiny systems, but even then often the hassle isn't worth it)
The overhead of spawning a process is not the problem. The overhead if your runtime is huge and/or slow to start could be, in which case you simply wouldn't run it on a serverless system - which is ludicrously expensive at scale anyway (my dayjob is running a consultancy where the big money-earner is helping people cut their cloud costs, and moving them off serverless systems that are entirely wrong for them is often one of the big savings; it's cheap for tiny systems, but even then often the hassle isn't worth it)