Postel's Law sounds nice but it can result in major problems. It results in a de facto spec that differs from the written spec, and disagreements about what a piece of data actually means can lead to bugs and even security vulnerabilities.
Having strictly parsed HTML from the start would be fine. You'd check it before you ship it and you'd make sure it's valid.
Requiring it now would be a disaster, of course. There's so much malformed HTML out there. But making HTML parsers accept garbage at the beginning was the wrong choice.