Instead they have a weird patchwork of bilateral treaties that are designed to look pretty much like EEA membership if you squint just right, and look like just bilateral treaties in separate areas if you squint a bit differently. They're linked, and at least the first seven have a "guillotine clause" so they all cease to apply if one of them is canceled, so in practice Switzerland is practically like an EEA member, but they get to pretend it's all very different.
There are some clear differences, though, and there have been years of negotiations trying to reduce them without success.
EDIT: No, I'm wrong; while EFTA Court used to be based in Switzerland, Switzerland is no longer subject to it. It still exists, but only for EFTA members who are also EEA members. This whole thing is impossible to keep track of.
https://en.wikipedia.org/wiki/File:Supranational_European_Bo...
And the GDPR scope is determined by the user, not the company. You can have your company based on the far side of the moon, with 99.99% of your users based on mars. For that one user that is living in Europe (note : living, not nationality) the GDPR applies.
Mind you, I'm not sure that the GDPR says that you can't charge for that. As long as you can justify that the amount is in relation to your expenses, my bet would be that a judge will allow it.
These GDPR conversations tend to pointlessly go back and forth on this because one side is describing the GDPR from the point of view of: what does the law say? The other is looking at it from the point of view of: I only have to follow my country’s laws.
The latter is closer to correct in some technical sense; laws have finite jurisdictions. But the EU has a big market and so lots of entities play ball with them, to some extent, in general, so it is probably better for most people to comply.