I'm not saying post season and championships are a hard requirement for HOF, but it absolutely matters to me. The best players do it on the biggest stage. Especially pitchers. It's no accident that Morris pitched for so many winning teams and in so many meaningful games. HOFer.
It's actually exactly that, an accident of his pitching well for good teams, and the fact that he wasn't actually better than his contemporaries that didn't have that advantage is why he shouldn't be in the HOF (or if you want a really big hall, those guys should be in as well). Jamie Moyer's post-season line is very similar to Morris', except that he had only half the opportunities and was substantially older. Blyleven's numbers in the post-season were better, again in half the opportunities.
Blyleven's career was more than twice as valuable to his generally poorer teams than Morris' was to his. Ignoring the final 4 years of Blyleven's career, in the first 18 years of his career (to match Morris' 18 years), Blyleven pitched 400 more innings, struck out 800 more hitters, threw 49 more complete games and 27 more shutouts, walked 200 fewer, gave up 26 fewer HR, and had an ERA of 3.14 compared to Morris' 3.90.
Even comparing their whole career's, Blyleven had better rate stats for everything, despite throwing 1000 more innings. If Blyleven had pitched for the mid-80s Tigers at the peak of his career, he'd have 300 wins and would have sailed into the HOF on the first ballot.