> $120K isn't going to cover the fully loaded costs of an SRE who can set up and run that.
> Hiring 1 person to run the infrastructure means that 1 person is on-call 24/7 forever.
> If there's an issue with the server while they're sick or on vacation, you just stop and wait.
Very much depends on what you're doing, of course, but "you just stop and wait" for sickness/vacation sometimes is actually good enough uptime -- especially if it keeps costs down. I've had that role before... That said, it's usually better to have two or three people who know the systems though (even if they're not full time dedicated to them) to reduce the bus factor.
So the entire business was happy to go offline for 2/3 weeks whenever their infra person fancied going off on their summer holiday?
By doing this, you're guaranteeing a bus factor of below 1. I can't think of any business that wouldn't see that as being a completely unacceptable risk.