What it would do, is unjustly cast suspicion on all the unmarried without solving the problem. Those men who genuinely believed in the value of celibacy and wished to remain in that state would have the added burden of being considered shirtlifters.
Your solution might solve the problem if only married men were allowed in the priesthood, thus doing away with the celibate state entirely. That would be lamentable.
Put me in close, day-to-day contact with a group of young men for several months or even weeks and I will tell you which of them has homosexual tendencies, or your money back. And I'm not even a spiritual director.
As opposed to ALL priests being considered shirtlifters today? Look, the Latin Rite priesthood is in a fix that it won't get out of for some time. Ordaining married men should at least be discussed, given the response of those same men to the permanent diaconate.
You are so right. It would place a great additional burden on those priests that were truly seeking to be like Christ.