Yes it is but people have been trying to do that for 40 years and have not gotten it right yet so...
Wrong. Plenty of code correctness has been deployed in service of this goal.
Unfortunately, there are endemic economic and political reasons why we constantly choose the protocols and implementations that are bigger, hairier, and less continent.
All you need is a culture of kicking non-conforming implementations to the curb, and then the rigorous implementations have a chance to emerge from the weeds. Do we have such a culture? No—most of the time—no, we do not. Such a culture would cramp Megacorp style, and interfere with timeless value-adds, such as embrace and extend, closed ecosystem, DRM jungle, NIST-sanctioned algorithmic weevils, definition by implementation, documentation by implementation, etc. etc.
Far, far away in dull and dusty places like the Erlang OTP or Bernstein's qmail or Knuth's TeX—or perhaps even the Google protocol buffers for at least one lucky and unusually blessed language binding from the somewhat recent past—you just might find a rigorously coded parser or two.
For the most part, however, I agree. We'll probably never have rigorous parsers in a dominant culture of "screw everyone else", Wild West dysenteroperability.