The military readiness argument is a familiar one.

It was used in 1948 when the issue was opening up the military ranks to blacks (impairing “the morale of the Army at a time when our armed forces should be at their strongest and most efficient,” warned Senator J. Lister Hill, Democrat of Alabama); in the 1990s, when the issue was allowing women into combat (“females have biological problems staying in a ditch for 30 days because they get infections,” said Representative Newt Gingrich, Republican of Georgia); and in 2010, when the issue was allowing gays to serve openly in the military (it would “harm the battle effectiveness which is so vital to the survival of our young men and women in the military,” asserted Senator John McCain, Republican of Arizona).

Now, Mr. Trump is making another grab at the readiness defense. The American military, he said on Twitter, “cannot be burdened with the tremendous medical costs and disruption that transgender in the military would entail.”

Critics of allowing transgender service members in the military say they will indeed add to overall medical costs and increase the number of active duty personnel who are out of commission for medical reasons. They point to Army statistics indicating that, at any one time, around 50,000 of the service’s approximately 500,000 personnel are on some manner of sick leave, with reasons ranging from a bad knee to maternity leave. That 10 percent nondeployable rate, commanders say, affects readiness.

Because many transgender people undergo hormone therapy or surgery to transition to the gender with which they identify, these service members often need more medical care than other military recruits.