While we don't advertise ourselves as service dog trainers, per-say, although we can teach some tasks (it's a lot like trick training) we are super into public access training. That is one of our specialties and something we take very seriously! We have clients and friends with service dogs who save their lives regularly and who have also experienced the very real threat of untrained dogs in public spaces. Just because you feel like your dog should be allowed to accompany you anywhere, doesn't mean they're actually qualified. To ethically do public access, your dog should be able to remain neutral and under your control in just about every variety of setting you can think of. With distractions like dogs, people, kids, shopping carts, loud and unusual noises, etc. Because if your dog is posing a threat to other people and/or to service dogs, it shouldn't be there. Service dogs are medical equipment for their disabled handlers, like an oxygen tank. You wouldn't want to go snatch someone's wheelchair away from them, right? So don't interfere with service dogs, because it is that serious for many handlers.
Whether you can function without a service dog or not is between you and your doctor, but how your dog affects everyone else when you take it into public shouldn't be up for debate. If you want your dog to access the public, make sure they are adequately trained to do so without being a liability or causing a nuisance or to anyone.