If you follow the 5 to 6 encounters per day, the paladins will lack spell slots very fast. Also, a paladin should declare his intention to smite before smiting. If he misses, then a spell slots is wasted.
In addition, make certain that fights lasts longer than 4 or 5 rounds (my average is around 7 with some fight lasting some 15 to 20 rounds!). This way, smite spells start to have a true appeal.
A lot of 5ed being easily abused is the fact that so much is hidden in plainsight. The 5 to 6 encounters per day might stink for some, but they can easily be incorporated into the narrative with simple explanations and narrations. The noise of the fights attract the next set of enemies or a patrol just happens to be returning exactly at the same time the last enemi of the previous encounter falls. If fights lasts longer and these fights are a bit more numerous, I guarantee that paladins will think to use their smite spells a lot more more instead of burning spell slots for a temporary spike in damage.
YMMV, but this is what is happening in my games.