would any of the big names in tech have a chance at being elected president of the US?

No.

As far as maximizing altruistic impact goes, would it be a good idea for them to become president? ... Do these people care about maximizing altruistic impact?

The impact of what? The whole of the US policy? That's an unrealistic goal. Besides, I don't know if any of them is particularly altruistic. They have lots of money which means that giving away large (in absolute terms) chunks of it leads to zero marginal impact on their life, but that's a different thing.

I also find it... ironic that Bill Gates is missing from your list.

What other "sane" people have enough reputation in the public eye to have a chance at acquiring a lot of political power?

You're thinking technocracy and that's not necessarily a good idea. What you want above all in a political leader is that his value system be aligned to yours. If it is not, the fact that he is effective at reaching his goals becomes a threat, not a benefit.

It is also the case that the US political process is set up to filter away the sane people. Would anyone sane really want a team of competent and malicious lawyers and investigators to go through his entire life with a fine-toothed comb looking for any dirt (or for what can be made to look like it)?

P.S. You should distinguish between actually running for Presidency and "let's pretend I'm running for President because it will be fun and I'm an attention whore, anyway".