I have a few dulcimers & some have 3 strings & some have 4 & one has 5 & one has 6.
The ones with only 3, I took one of the melody strings off because I finger pick with one of the dulcimers & the other just sounded better with 3.
The ones with 4, sound good that way & I don't have any trouble with pull offs, hammer on's is still a problem no matter if it's 3 or 4 strings. Still working on the force & position to the string, also which finger works best & depending on where my fingers need to go afterwards.
As everyone is saying 'personal preference ' but also the dulcimer may have a say in what works best for it. If I was building a dulcimer I would go with 4 strings, that way the player can decide what they think works best for them.