Email is actually a tremendous, decentralized, open platform on which new, innovative things can and have been built. In that way, email represents a different model from the closed ecosystems we see proliferating across our computers and devices.
Since the emergence of productivity software in the 1980s, it was sufficient for a long time to entirely focus on features (1st wave of differentiation). This is not surprising as a large value could already be created by adding desired features to very rudimentary software products.
The app that comes closest to a luxury service that I can think of is Superhuman, which charges its users $30 a month for an email client (which you could also get for free by just using Gmail).