You are a living example of unix brain damage
Just because what it does internally need not be trusted does not mean the output, or even input, to it is so. Say you input text into a program you don't trust and out comes a fork bomb on a unix system. Well even if your entire system were perfect and that mythical fork bomb on such a system didn't do shit that doesn't change said program can affect the cycles your proccessor had to go through transfering the information from one place to another. From which information can be gleaned, i.e a side channel.
They can't. Use static memory as dynamic has side channels inherent by design. You will always have a cache of some sort for what physically goes to what virtually in dynamic memory models. Even if you had a device, like a second set of RAM dedicated to cache storage that is physically seperate from everything else, that physically stored the cache on said device and did not allow access except via certain methods, there will always be some way of accessing that cache which is a inherent side channel.
Sure you could take a hypervisor like the linux kernel and say only this region the linux kernel inhabits in RAM somwhere has commands to physically jump to the off device MMU cache, it is still accessable. Schedulers will always take control away from something else you do, unless you control the scheduler. So don't have any schedulers and if you do you must have control over them. See the specter vulnerabilities for proof of this fact.
Also wtf I just got the same captcha from like four times ago.