Another vote from me to make it a free action to cast with a "once per turn" (or once on your turn) style limit on it. This achieves the intent of limiting/mitigating the multi-smite-alpha-strike concern (a concern I truly get, being known as the one-round boss mage killer in the PotA campaign playing with a 2014 paladin) while allowing the paladin to play nicely with all weapon use cases that might also use a bonus action, letting them retain their martial warrior archetype.
(As an aside, and while there are other considerations and effectiveness to consider, strictly looking at smites a 9th level Warlock w/ 2 short rests in a day can deal out 36d8 smite damage. Paladins using all their spell slots + their free casting only get: 27d8. With only 1 short rest, the Warlock can still deal 24d8 extra damage, and at a higher alpha strike too of 6d8 vs the paladin's 4d8.)