"Influenced" might be a fair word though. The ability to exert influence, any influence at all, can some times build up to a potent attack in unforeseen ways. Hell, look at Rowhammer and how that works. It's nuts.
I figure there will be some use cases where it would be super bad to let an attacker exert any influence on your system whatsoever, especially if paired with simultaneous attacks that synergize with a prompt attack, like for example if a prompt attack + user database can be combined with a side channel analysis like thermal data or something, and used to learn information about private keys on the server.
My overall point is that many prompt attacks may not meet the bar to be a "hack" but they certainly constitute an attacker being able to exert an influence on the running server, which can potentially allow sandbox escape when paired with other vulnerabilities. Which to me, is potentially pretty scary given the bad possibilities of what evil rogue AI can do when it is in the role of the offensive hacker, and can battery away at sandbox defenses 24/7/365 until it finds a sandbox escape. Meanwhile, the AI may cover its traces by falsifying the records of computational resources used. It is to be truly a frightening thought and one I hope we can all work hard to avert. We can do our part by being extremely EXTREMELY diligent with cyber-security, hardware security, software supply chain traceability & governance, and so on.