I see your point, but I think it's fundamentally flawed: I think the very reason we can look at this and go, "it's just rental cars with an app" is because it's not all that innovative. Beyond that, these regulations exist for a reason, and if they're going to be argued against then it's on the part of the "innovator" to build a business model that distances them, in granular operational detail, sufficiently far from the old model to make those regulations irrelevant.
e.g., Do I also feel that if someone creates an airbnb for food production that they should still be required to comply with all the regulations of the food prep industry? Yes, I do. They're still putting food in people's mouths, and the bulk of the regulations exist to protect people who are eating strangers' food. IF their business model is so divorced from the old restaurant model that the risks the regulation addresses no longer exist, I'd be more sympathetic, but I've yet to see that be the case.
In this case, for instance: I'm interacting with you, the app, and buying a ride. You're selling me a ride. For the same reason we have food safety regs, you're required to make sure your fleet is safe and up-to-date. Why, precisely, would you be exempt from that just because you source your fleet differently than a traditional rental car company? There's nothing about the app/service that negates that concern. The business, in the relevant respect, is the same - so why should they get a free pass on the regs? Because they've chosen a different model for sourcing cars?
Fundamentally, no one is owed a business model. IF your business model is "same old business, peer sourced supplies, and an app" - that is to say, in most functional respects the same business that is already regulated - then yes, you should be subject to those regulations. The very fact that these business are so very easily slotted into existing regs is because they're so similar to existing businesses. AirBnB didn't have trouble with regs when it was actually people letting spare rooms; it ran into trouble with regs when a large percentage of their rooms came through single owners of multiple dwellings dedicated to airbnb. That is, when they became a hotel.