I don't think Rust holds much potential over C in terms of exploit payloads. The closer you are to the hardware the better; any abstractions will only get in the way. For the exploit payloads C is probably where it's at.
Rust is well-suited for writing custom tooling, incl. for vulnerability discovery; see https://github.com/kpcyrd/sniffglue or or https://github.com/kpcyrd/sn0int or https://github.com/AngoraFuzzer/Angora for examples of such tools. Specifically, Rust is good for tooling you're going to use long-term and need it to be dependable; not very good for rapid prototyping.
I'd rather not talk down other peoples work and instead recommend tools that match "Open-Source, Free-use, non-subscription-model tools":
- sn0int (see also r/sn0int, disclaimer: I'm the author)
- Maltego CE has a free trail but isn't opensource and requires a registration
- recon-ng is similar to sn0int, might be worth a look
You might want to have a look at sn0int. It saves you some work since you only need to write modules and the engine takes care of everything else, but you might should make sure the data you're trying to collect fits the database model.
I've accumulated a large amount of feedback for sn0int when it went popular on r/netsec that I'm still working on, but I managed to hit a compiler bug and I'm currently considering pausing development because I can't push new releases due to this.