eBPF does have loops and it is absolutely for general purpose computation.
The verifier that exists in the Linux kernel works very hard to make sure that you are not allowed to load programs with unbounded loops but you most certainly can when those restrictions are lifted.
This is trivial, when people talk about eBPF they are talking about the implementation, its like saying you could put lisp code in C, if only you modified the C compiler.
The implementation that exists in Linux is perfectly capable of running unbounded loops. But it runs your program through a function that rejects your program if it can't prove that it terminates.
The point being that you could rip the eBPF implementation out of the kernel, remove the verify check and have a very usable VM.
The verifier that exists in the Linux kernel works very hard to make sure that you are not allowed to load programs with unbounded loops but you most certainly can when those restrictions are lifted.