. Without meaningful work to do they would tend toward a life of inactivity and reproduction. These people would reproduce >like pets that are not neutered. Their population will grow creating an increasing burden on an ever smaller percent of the ? >population that remains competitive
There is no data or evidence to suggest any of this is true. This is your hypothesis which no statistics back up. For example in developed nations where people are poor there isn't evidence that as the standard of living increases the rate of reproduction goes up. In fact it's the reverse where the higher the standard of living gets the lower the rate of reproduction.
The other myth is the idea that all meaningful work has to be working for food or for survival. The truth is the most meaningful work appears at least in history to be when people actually aren't concerned about survival. When people are at times of peace rather than war you get a Renaissance or an Enlightenment.
Finally, there will always be work for humans to do even if it only pays pennies and is microwork. AI has to be trained. AI has to evolve with humanity and that means the AI has to interact with humans, collect or buy data from humans, and in the end in my opinion humanity and that AI will merge. Cyborgization is the process of the merger between human intelligence and artificial intelligence into a unified IA (intelligence amplified) cyborg.
To understand more you should watch some videos from Hugo De Garis. I encourage all to watch his series of videos if you haven't.