I bought an almost new semi-grand harp just for rehearsals, practicing and small gigs. I decided to dedicate my good concert grand that I used for a recent recording for big occasions. Why have someone else put wear and tear on a harp that is special to you. I would have a teaching harp unless you are playing on a harp you don’t care about.
Many teacher who I know have several harps, some of which they purchased as student rental instruments. In a few instances the student has an option to buy it. I suppose it depends on the teacher and the prospective students but for many a decent lever harp or two is a good investment. And/or as Gretchen says a smaller pedal harp can also be nice to have.
If you teach both lever and pedal, it only makes sense to have both available during lessons. I had a teacher who only had pedal harps. I only had lever. So I would practice pieces with lever changes all week at home, and then not know how to make the pedal changes during a lesson, since I couldn’t practice that way.