would like to have done

According to Garner's fourth edition,

'd have liked to should be followed by a present-tense infinitive, so 'd have liked to (٭have done) is wrong; nor is correct 'd like to have done because the sequence of events is then off.

What does the author mean exactly by the sequence of events is then off?

As I understand the sentence quoted, I disagree with the author.

All the versions are valid and have different meanings.

Examples

1. I would have liked to see Australia.

When I was younger, to see Australia is what I would have liked. Now that I'm older, it isn't what I would like because I don't like long plane journeys.

2. I would like to have seen Australia.

I would like now to have seen Australia in the past.

3. I would have liked to have seen Australia.

My memory is failing but I'm pretty sure that, when I was 30, I would at that time have liked to have seen Australia when I was 20.

In real life, people don't make these distinctions and you will hear all three versions. What people usually mean is, "I wish I'd visited Australia when I was younger"