The problem is that roughly half the population is fighting against this kind of social welfare system and they would only be encouraged by PG's blog post.
Or, importantly, to do menial work on things that were previously considered not as important or productive as what they were doing menial work on.
People always assume retraining means you have to learn a technological job or something else absurdly out of reach. A lot of the time it just means doing the same or similar thing you were doing, but in another context that has now become relatively valuable enough to devote labor to now that this other thing don't require it.
And, as you hint, being able to create a lot of value without a lot of ongoing cost is a pretty key step towards basic income (of which the "leisure economy" is really just a more extreme example). Having that would indeed offset the issues of those who can't or won't transfer skills.
The more that we can do this, the more surplus wealth we create. This is clearly working by reference to history: this is the best time ever to be poor, compared to all points in history before it.
This isn't quite so obviously true, but it's likely also the case that an unemployed person today has significantly better life outcomes than a menial worker 100 years ago (which means mines or factories). That's what improved automation buys us.