Who should be running for government? Because of its nature it seems it will always attract less than the best people

It seems to me that the people who should be in government wouldn’t be there. And instead would be running companies and actually productive ventures. Which being an elected official in government. Besides it escalating your chances of assassination. Isn’t the most interesting or “productive” job like discovering a new medicine or inventing a new machine.

Because of this it seems that at best you will always get the second runner up instead of the people who should actually be there.

Which I think this problem infects other government positions aswell. Like the people who become generals or even police officers. Which seem to attract the same problem of less than ideal people. Because of the nature of the job.

So who should be running for these positions? And is there a way to beat this pervasive incentive structure of attracting people who are not the best producers but the best destroyers or at the least people who would not be top producers.