Every chromatic dulcimer comes with a free diatonic hidden in plain sight. Ignore the extra frets until you need them. For some people this is no problem at all. For others it's confusing and it sounds wrong and they just don't like it. Either opinion is perfectly valid. It's your dulcimer.
I play chromatic. I play diatonic. I play half-breeds with 1.5 and 6.5 frets. Since you asked why NOT buy chromatic, here's what I got:
Chromatic is harder to play. It has wrong notes. This is not insurmountable. Think about the guitar players you know; are they all rocket scientists? If they can manage a chromatic fretboard, so can you. However, if you hate to practice scales you will probably be happier with a diatonic.
Noter speed bumps. Do you play with a noter? Can't stand the idea of your dulcimer sounding like a slide guitar? This is a dealbreaker for some. And some could not care less. Know thyself.
Lack of instructional materials. This is a big one. There are a few books and videos for learning chromatic dulcimer, but not nearly as many resources as diatonic. When an absolute beginner asks me about dulcimers, I usually steer them toward diatonic.
Modal scales get difficult. Dorian is my favorite mode for improvising, and it's so easy on a diatonic! Dial in the right tuning and off you go. Whereas learning all the scales on chromatic is a major learning curve.
Other dulcimer players fly into a panic. Seriously. A friend gets a dulcimer and wants to play together. Bring out a chromatic and they'll yelp in terror. It doesn't look the same. It's too complicated! I have to keep a diatonic around or I won't have any dulcimer friends.
It's not traditional. This matters to many people. And sometimes (living history events? tapping into your personal memories of dulcimers past?) it may matter to you. If the sound you fell in love with is the sound of a traditional silvery noter/drone modal dulcimer, a chromatic is unnecessary and will make it harder to replicate that old-time sound.
That said, if you already have a diatonic dulcimer and you're considering chromatic, and if you have the time and inclination to learn something new, then my advice is go for it.