@BohemianPeasant the misunderstanding is that no, the Constitution doesn't impose that bar. It only authorizes the bar, but the Constitution itself always relies on others to impose such stipulations.
For any constitutional concept to take force there has to be some functionary interested in giving it life, whether Congress through, say, EC processes or the executive branch through execution of law, or courts through judicial processes.
The Constitution does NOT impose the disability. It can't. It's only a piece of paper spelling out rules.
It's up to others to impose the rules, and that's exactly what the Supreme Court recognized in its ruling.