David N. Friedman writes:

"The experience of King David and Solomon is understood by all to equate
with no permission slip to have concubines, David was punished for his
behavior."

David didn't have concubines, unless you count Avishag who was sent to bed him in I Kings Ch. 1 in a futile attempt to prolong his life. Otherwise, David had multiple wives, which was permissible at the time, polygamy not explicitly being an offence until Rabbeinu Gershom's ban (which Mizrachi Jews ignored). What David was punished for was not concubinage but adultery, and murder for the purpose of covering up said adultery.