Who said that? I would ignore them. Live patching just means that your OS updates while it's still running. To answer the question: Raspbian doesn't do that out-of-the-box, you have to restart it after an update (I haven't updated or even restarted the Pi in several months).

Ubuntu and a lot of Linux has the option if you use Ubuntu Pro, but I update my OS so rarely it's a non-issue. I wouldn't even consider that when comparing on-prem vs cloud.

My hunch (and as someone who uses both daily) is that on-prem is 2-10x faster than affordable cloud options within a region, but in some cases like international traffic or high-end multi-core computing etc. cloud should pull away from on-prem - but curious to see what you find :D