Eliminate ambiguity (and several classes of exploits):
It's easier to "start small" (i.e. with a short binary encoding) that won't be much ambiguous in the first place, than to try to add restrictions (and thus additional complexity) to a freeform text protocol. Or put another way, instead of adding error cases, it's better when there are no error cases in the first place.
Encode certificates with human-readable JSON instead of ASN.1 DER.
Hell no. DER is prefix length-delimited, JSON (and text in general) is not.
This means that unmaintained software will stop working after 2 years.
Hell fucking no! The last thing that anyone who cares about things working wants is planned obolescence and even more constant churn (which just leads to more and more bugs.) If anything, that will only make the "handful of implementations" of TLS turn into perhaps one (i.e. Google's), or maybe two at most. Thats even worse.
Replace TLS. It is mind-numbingly complex.
Replace it with what? Your proposal essentially reinvents the main pieces of TLS (authentication, confidentiality), and TLS is already quite modular with respect to that.