1. Why do people have to fix their mistakes if automation can solve the problem for them?

Postel's Law isn't about automation, it's about where to apply effort. Automatically fixing mistakes at the time of their creation would be great, but just like real life, there are a million ways something can be interpreted wrong after the fact (and thus the wrong "fix" applied) and only one way to interpret it right.

why should we force humans to jump through hoops?

Humans have to jump through hoops to create the robust error recovery. Rather than the effort being evenly distributed among all parties when everyone is conservative on both the production and acceptance side, the producers can be really lazy and the acceptors have to jump through hoops to accept all the lazy people's output. There is no automation here, someone has to write the code that liberally accepts things, which is often a hard task because of the many different ways things can be interpreted when they are not specific and explicit.

2. Why can't a parser be strictly standardized and liberal with its input at the same time? If the spec provides error recovery behavior, what is wrong with that?

A parser that is liberal with its input and provides robust error recovery begets tag soup. The only people who like tag soup are those who want to be lazy when producing it. It's more work, over all, to accept all input and try to figure out what was intended than it is to just say "I can't interpret this" and tell the generator that they need to be more conservative in what they generate (the other part of Postel's Law).

My point is that there's no such thing as too liberal as long as all parsers implement the same exact kind of liberal parsing.

It's not the liberal parsing that is necessarily the problem, it's the second order effect of liberal interpretation. If people can be liberal in their parsing, then they can be liberal in their interpretation, and if we accept that, we have to, as users, accept very little robust interoperability.

Our low-level communication protocols have no concept of invalid input, they can recover from any random burst of garbage input

"Recover"? If you don't do the TCP handshake in very specific ways, not only does no other server talk to you, but you may end up breaking some of the guarantees that TCP is supposed to provide. Random garbage that sets the RST bit in a TCP packet closes the connection, it doesn't "recover" from that.

Now, obviously, I'm not advocating that things should outright crash when given bad input: that's the worst. They should produce decent error messages as soon as possible so the producer can increase their conservative nature of generation. Consider serving a web page as application/xhtml+xml, which in Firefox (at least back when I was doing a lot of this) would fail to accept the file and would tell you where it was structured wrong. By accepting any old ambiguous format, you'd never see this error and you wouldn't know that you weren't being conservative in your output. And since different browsers treated malformed content differently (either accepting it, or not accepting it, or trying to guess and often getting it wrong or different from what other browsers guessed), you end up with a mess where the "liberal" accepting side gets tagged as deficient if it doesn't jump through all the hoops thrown at it.