In fact, the ability to encrypt directly with RSA is probably a bug, not a feature. There are too many ways to do it catastrophically wrong, and it almost guarantees cryptosystems without forward secrecy.
(WebCrypto isn't great and I'd avoid it, but this isn't why).
Do you have a link to a discussion on why WebCrypto isn't great? More specifically, are you saying there is no real good way to do encryption with WebCrypto, or is it that it is too easy to do it wrong?
It can make some sense in extensions, or in situations where client-side cryptography is more an interoperability or offloading concern than an end-to-end security concern. But ultimately, it's misused more than it's used well.