I love the idea of this because I hate lawn maintenance. But the idea of letting software I wrote run around with whirling blades of death underneath of it would keep me from doing it.
Can also confirm about the zero turn mowers. Recently switched jobs from automating cars/tanks to mowers myself. At the very minimum mowers have way tighter power and space constraints plus hydros are not easy to control well automatically.
That's the approach most industrial robots take - instead of trying to deal with humans and not hurt them, just make sure there are no humans within reach of the robots.
That's harder than it should be. No amount of asking my neighbors has kept their kids out of my fenced lawn to retrieve their soccer balls. Which is actually an issue because one of my dogs is not particularly friendly. I'd gladly kick the ball back over if they just knocked on the door. We're not a neighbor-hate-neighbor situation, we actually get along quite well, but kids will be kids.
It's up to you to run the numbers whether the cost of securing the area is less than what you spend (in terms of time/inconvenience/etc) manually mowing the lawn.