> Pick any programming language. Now, remove access to I/O (except standard input and output), networking, time, random number generators, threads, OS syscalls, etc.

The devil is in the details, and if you miss even one case then the problems are just as bad as if you hadn't bothered at all. For example, comparing two URLs in Java is not deterministic. For another example, iterating through a set in Python will give you the elements in a different order on 32- versus 64-bit systems.

In practice it's just not practical to retrofit deterministic behaviour onto a language that was not designed for it. Even your "trivial example" isn't; Brainfuck does not standardize overflow behaviour and so the same program may behave differently on different systems.