I would say 30kph would be plenty especially for nonstop on-demand service. 60kph sounds unrealistic.
The reason I think you could lay new track is that kiddie train track is really cheap and used railroad rail is pretty valuable.
The value of a scrap railroad track varies by material and its condition. Depending on its dimensions and shape, a ton can range from $300 to $750. For example, an R50 track will fetch a price of between $200 and $750, while an R65 way will cost more than twice that.
It would be simple to make self driving golf carts that followed a magnetic or inductive guideway or even used a virtually guideway with gps. There are a few of these available off the shelf right now. One I remember is dutch and there was another produced in Great Britain.
Rail is hard to steal because it is hard and heavy. Look at the price of small sections used for anvils. It was a shock for me.
I participated in a exploration of PRT that was done by someone at University of Washington a few decades ago. One of the things discussed was the comparison of travel times between slow PRT and fast light rail. It doesn’t take many 60-90 second stops to really slow your average speed.
It’s kinda like that brain teaser: If a race car does the first lap at 60 miles an hour how fast does he have to go on the second lap to average 120.