If you're ever stuck wondering why a bunch of smart, motivated people with no clear corrupting motivations are being idiotic, that's a strong heuristic that you should spend a bit more time analyzing the issue, IMO ;). "Ugh, why is everyone else so stupid" is a common take for undergrad engineers, but I'm sure you've grown out of it in other ways. Anyway, more substantively:
The simple answer is that people have thought about it in depth, most famously noted doomer Eliezer Yudkowsky in Intelligence Explosion Microeconomics (2013)[1] and its main citation, Irving John Good's Speculations Concerning the First Ultraintelligent Machine (1965)[2]. Another common citation that drops a bit of rigour in the name of approachability is Nick Bostrom's 2014 Superintelligence: Paths, Dangers, Strategies[3].
[ETA: to put it even simpler: a system that improves itself is a (the?) quintessential setup for exponential growth. E.g. compound interest]
For the time-bound, the most rigorous treatment of your concern among those three is in Section 3 of Yudkowsky's paper, "From AI to Machine Superintelligence". To list the headings briefly:
- Increased computational resources
- Communication speed
- Increased serial depth (i.e. working memory capacity)
- Duplicability (i.e. reliability)
- Editability (i.e. we know how computers work)
- Goal coordination (this is really just communication speed, again)
- Improved rationality (i.e. fewer emotions/accidental instincts getting in the way)
Let's drop "human" and "superhuman" for a minute, and just talk about "better computers". I'm assuming you're a software engineer. Don't you see how a real software dev replacement program could be an unimaginable gamechanger for software? Working 24/7, enhancing itself, following TDD perfectly every time, and never ever submitting a PR that isn't rigorously documented and reviewed? All of which only gets better over time, as it develops itself?
[1] https://intelligence.org/files/IEM.pdf
[2] https://vtechworks.lib.vt.edu/server/api/core/bitstreams/a5e...
[3] https://en.wikipedia.org/wiki/Superintelligence:_Paths,_Dang...
TL;DR May God have mercy on us all.