As I thought my post made clear, the best system for union elections is one that protects workers' rights:
(1) Workers' right to unionize is protected against management intimidation by fair election rules that are actually enforced.
(2) Workers' right not to unionize is protected against union intimidation by a secret ballot.
It's misguided, however, to make a fetish out of point (2) while ignoring point (1). As long as management is permitted to get away with just about anything, card check can reduce the effect of intimidation by management. Back here in the real world, management misconduct is a much greater problem than union misconduct. A secret ballot isn't much protection if management can fire anyone who even tries to organize a union in the first place. Under those conditions, you won't have a secret ballot because you won't have a ballot because no organizer will last long enough to get signatures on the required number of representation cards.
The present dysfunctional system would be better with card check than without it. The best system, however, would include a secret ballot AND some changes in the NLRA combined with enforcement of current provisions of the NLRA that are now widely flouted.
Any analogy to public elections has to be considered in light of the question: Does this analogy make sense in a context in which one side (the equivalent of one political party) can fire voters it doesn't like?