Would people with a basic universal income lead to many more people deciding not to take paid employment? We must assume it would.

Your assumpton would be in error unless you could guarantee that the UBI would be sufficient to fund all expenses and that rigid price controls would assure us that such would remain true. One only has to look back as far as the pandemic to understand that inflation is not something we can assume to be constant or that business wouldn't use it to provide cover for extreme profit increases without incurring the cost of increasing output.

If you presently received Yang's $1000 monthly check from the government you would still require some way to aquire the rest of what it takes to live. Your employer would remain as much in control of your life as it is presently, only the cost of that control would now be $1000 per month less because it would know you have that guaranteed from the government. Any possible method of distributing a UBI will face this inevitable outcome unless the issuing government assumes total price control in the economy, something extremely unlikely in our monopolized, corporate controlled, economy.

As soon as such a payment is distributed to everyone (the only way to make it politically acceptable) it faces the problem of inflation until it is consumed by increased profits, nulifying its purpose. Raising prices to capture $1000 per employee is no great feat for our capitalist overlords. I would predict that the gains made by labor would be absorbed by capital in the first year after implementing such foolishness.