I remember someone posting in a recurring revenue thread on HN about a similar service for medical doctors some time ago, was that your inspiration?
Edit: and a different linguistic area
Why not? Well, you have to have very standardized services which the customer understands to adopt a booking solution. For example, if you're a customer and can say "I want a 45 minute shoulder massage from Cindy", then Cindy's shop can use a booking platform. Most AR customers can't, because the client can't predict how long a dental appointment last, doesn't know that Joe can't come out to his house unless Frank gets the van back in time, etc etc. This is disproportionately the case for upmarket services businesses, which is where AR is moving. (e.g. We want customers with a $100+ value per appointment -- more "professional services" like accountants/medical/HVAC than "personal services" like hair care/massage therapy/etc.)
(I should mention that, even in the hypothetical case that a HNer were in direct competition with AR, I'd be more than happy to see other options available.)
The problem you've listed (not knowing how long a dental appointment will last) isn't really a problem for a booking system...a dental office with a receptionist scheduling patients will run into the exact same issue and the same rules that the receptionist uses can be programed into a booking engine. The bigger problem for a dental office is that the calendar is locked in a management system that's probably running on a Windows computer somewhere in the office. Maintaining two calendars is almost never going to work and the one in the cloud will never be the calendar of record. Short of going the ZocDoc route and having practices reserve certain spots for appointments booked online (businesses hate doing this), you're always going to run into problems with conflicting appointments. The interesting thing is that most dental practices won't care about conflicting appointments since the only patients that will book online will be new patients and patients that have fallen out of the typical schedule. Everyone else will schedule their appointments with the receptionist at the end of their previous appointment. So most dental practices will happily juggle appointments to fit those specific types of patients into their schedule.
But that's the dental industry and almost every other industry has just as many quirks as the dental industry does, if not more. And that's why the market will most likely be filled with smaller, specialized vendors that target either one or possibly a handful of verticals. I'm betting the winners will be the companies that make the management systems used by the businesses, but that's not happening quickly since most of them are small ISVs that only understand Windows development and think cloud computing is something that meteorologists do.
I see it everyday: I work at a company that manufactures running shoes in Germany and the retailers we sell to are mostly small, very competent running stores for enthusiasts - not your average national chain like Runner's Point. However these stores barely have any digital inventory/order/customer management solution, use way overpriced point of sale systems and often resort to fax machines when submitting an order. Well, what I'm trying to say is that there are potential customers for useful niche services left and right. It's just not always very obvious.
What you're doing, looks great though.
Germany is horrible at e-commerce. There are still so many opportunities to "disrupt" this sector.