I have heard, but do not aggree, that Let‘s Encrypt is risky, because phishing sites use it. It’s implied that other CAs do checks against it.
The authentication must be done before the encryption parameters are negotiated, in order to protect against man-in-the-middle attacks. There must be some continuity between the two as well, since the authenticated party (both parties can be authenticated, but only one has to be) must digitally sign its parameters.
Any competing authentication scheme would therefore have to operate at a lower layer with even more fundamental infrastructure, and the only thing we've really got that fits the bill is DNS.
EDIT: A standard exists for this already, it's called DANE, though it has very little support: https://en.wikipedia.org/wiki/DNS-based_Authentication_of_Na...
We have clear and seemingly easy go-to examples like proving that yes, this is THE Microsoft, and not a shady fly-by-night spoof in a non-extradition territory, but apart from the headline companies--who as of late seem to like changing their names anyway--this actually isn't easy at all.
Walled gardens like app stores have different trade-offs, admittedly.