Is there a reason for levers to be reversed on bikes with hydraulic brakes?
It's not for hand signals. "Left hand only" signals were originally designed for cars. You couldn't use your right hand out the window, so you could only use your left. Using both hands to properly signal on your bike is far more clear. It's used on motorcycles due to the fact that the throttle is on the right hand, so you want to keep that engaged at all times.

Reversed brake routing (front on the right, back on the left) is called "moto" routing and is primarily used in MTB and cyclocross bikes. On a CX bike, it's done so you can have greater controlled braking with the left hand on the back brake while your dismounting your bike for a barrier and your right hand is on the top tube. The front brake offers more power, while the back offers easier minor speed control while approaching a barrier.

To answer your initial question, there is absolutely no reason the brakes cannot be switched on your bike. Either the mechanic is lazy or doesn't know how to work on hydraulic brakes. In either case, you should take it to another more capable shop.