At scale (like comma.ai), it's probably cheaper. But until then it's a long term cost optimization with really high upfront capital expenditure and risk. Which means it doesn't make much sense for the majority of startup companies until they become late stage and their hosting cost actually becomes a big cost burden.
There are in between solutions. Renting bare metal instead of renting virtual machines can be quite nice. I've done that via Hetzner some years ago. You pay just about the same but you get a lot more performance for the same money. This is great if you actually need that performance.
People obsess about hardware but there's also the software side to consider. For smaller companies, operations/devops people are usually more expensive than the resources they manage. The cost to optimize is that cost. The hosting cost usually is a rounding error on the staffing cost. And on top of that the amount of responsibilities increases as soon as you own the hardware. You need to service it, monitor it, replace it when it fails, make sure those fans don't get jammed by dust puppies, deal with outages when they happen, etc. All the stuff that you pay cloud providers to do for you now becomes your problem. And it has a non zero cost.
The right mindset for hosting cost is to think of it in FTEs (full time employee cost for a year). If it's below 1 (most startups until they are well into scale up territory), you are doing great. Most of the optimizations you are going to get are going to cost you in actual FTEs spent doing that work. 1 FTE pays for quite a bit of hosting. Think 10K per month in AWS cost. A good ops person/developer is more expensive than that. My company runs at about 1K per month (GCP and misc managed services). It would be the wrong thing to optimize for us. It's not worth spending any amount of time on for me. I literally have more valuable things to do.
This flips when you start getting into the multiple FTEs per month in cost for just the hosting. At that point you probably have additional cost measured in 5-10 FTE in staffing anyway to babysit all of that. So now you can talk about trading off some hosting FTEs for modest amount of extra staffing FTEs and make net gains.