I guess its supply and demand. But east coast dentists charge more than west coasters. You may have to look around and see if there are more afordable ones,but remember the cheaper isnt always better. Get a provider that has done a lot of cases to be safe.
Another concern with swimming with them in is if you take in a lot of water. The aligners COULD trap the chemically treated water around the teeth and over time may affect the enamel. Swimmers teeth is common with competitive swimmers and could be worsened with aligners. Maybe.
It likely DOES matter, but I haven't seen a gap that couldn't be closed with Invisalign. It may take longer than desired, but gaps can be closed well.