Two of the LA dealers in my area offer this service. But they do it more to sell LA machines then to make ends meet just offering rental service. Both also operate more traditional quilt shops with fabric and piecing supplies like rulers and such. They only have a very small inventory of LA supplies. Most LAQ that I know order their supplies on line or get them at shows but sometimes you are in a bind and need thread quick so turn to the shop.
I would think most people willing to pay the premium to rent a LA machine would expect the machine to be stitch regulated. The average stitch regulated LA retail price starts at around $8 to $9,000 for the lowest end machine. Most LA manufacturers would expect you to have several ranges of machine in house from low end to high end computer driven set ups. Especially if you plan on exhibiting at shows. Also most of the big manufacturers have established dealer territories already. Have you researched your area for LA dealers and for which brands. Oh yes, you would not be able to carry multiple brands to be a dealer. I am pretty sure all the LA manufacturers want their dealers to be exclusive to their brand (Gammel, A-1, Nolting, ABM Innova, etc) You are talking a minimal start up cost of at least $50K and that is probably a low end figure that doesn't include insurance, property rental, utilities, etc.
My issue with rental was I wanted to get good at longarming, an all over meander or simple E2E panto is all that can be completed in a few hours. The average rental time was $50 to $60 per hour after training. both dealers are over 1 hour drive so I knew I could never get the needed practice time in. for those that just want to get their quilts quilted... assume 3 hours rental for an all over meander on an 80 x 100 quilt will cost the average consumer $150 (figuring $50 per hour and they have already paid for training). They can send an 80 x 100 quilt out to a professional LAQ for an all over meander for anywhere from $80 - $120. It doesn't take the renters long to figure that out. So they either turn to sending out or start saving their money for purchasing their own.
The dealers in my area offer rental as a courtesy. A side line. For one dealer, their primary business is being an LQS because they have a large inventory of fabric and notions and also sell domestic sewing machines in addition to LA. In fact I believe the LA aspect of their business is just a side thing. The other dealer is primarily a long arm dealer. Most of their income comes from sales of machines but they also supplement with fabrics and notions. Seems to me if they could make or even break even by just renting time on their machines they would do so.