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.
They are actively being negotiated because both Switzerland and the EU have realised there's a need to reform the original treaties, and the EU for a decade now have insisted that anything replacing them need to be closer to the EEA agreement, while having made clear they're not doing this crazy thing again for anyone else.
I'm not sure how long the EU can afford to further alienate countries that pay net positive into it's wallet, after losing the UK and the continuing rise of euroscepticism.
The EU can afford to stick to its guns in this indefinitely. It's made it clear for a decade that any change to the treaties with Switzerland can contain minor concessions, but only in return for a bet reduction in the deviations from the EEA framework.
With respect to euro scepticism, that largely fell apart thanks to Brexit - most of the parties arguing for the same for their countries have moderated their stances significantly, and support for the EU increased massively. Including in the UK where Brexit is widely seen as a massive mistake, and it's more a question of electoral calculus (neither of the big parties can afford to alienate the Brexit diehards yet; they're spread across the political labdscape) than anything else when rejoining gets in the political agenda.
As an addition re: the reduction in euroscepticism, according to Pew Research, between 2016 and 2019, the proportion of people with a favorable view of the EU rose 26 percentage points in Greece, 19 in Germany, 19 in Spain, 18 in Sweden 15 in the Netherlands, 13 in France, 12 in Poland, 10 *in the UK, 6 in Hungary. In 2022, a EU parliament survey showed overall support for the EU across member states was at a 15 year high, also much thanks to the Brexit bounce. In 2023, the European Parliament Eurobarameter - Autumn 2023 survey showed 72% of EU citizens think that their country has benefited from being a member of the EU, and only 22% thinks it has not.
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...