Currently, both major political parties have paid employees who function as “upper management.” Would the type of person seeking such a job change if the parties were supported solely by public funds?
If this were to happen, the people who became “upper management” in the political parties would presumably be of lower quality, or at least of lesser ambition, than those who are there now.
It is typically true that public service attracts a slightly lower quality of employee, or at least a slightly less ambitious type. The sorts of salaries that can be paid by government agencies tend to be lower than what truly talented people with the same credentials could get if they worked in the private sector. The same is likely to happen if political parties were solely funded by the government. The salaries would drop and the sort of people who now fill those jobs would likely depart for the private sector.
It is, of course, possible that the parties would still get very high quality people. These people might be attracted by the thrill of being involved in positions of some power. They might hope to parlay that into high salaries in the private sector later on. However, it does seem likely that the lower pay would result in something of a decrease in the quality and ambition of those working for the parties.