I think it's safe to say that any pressure cooker will pop its safety valve if the situation exists for it to do so, unless electric models have a sensor that knows to shut things down if pressure gets too high. My guess is that cooking something that's not recommended and could block the vent tube, or filling the cooker too high have been the primary causes of safety valves activating on PCs over the years. A little common sense will eliminate the potential for a nasty clean-up job.
I have stove top cookers in sizes ranging from 4-quart to 10-quart. They are much easier to use on a gas burner than electric, unless you have an electric burner with infinite heat range adjustment. I agree with the statements above regarding preparation of meats like a big shoulder for pulled pork. So much faster than in an oven. I've made luau-style kalua pork shoulder in the PC a couple of times, and it has been perfect.
The only baby sitting I do is in the beginning, waiting for the weight to start rocking and then adjusting the flame down. After a few minutes spent tweaking the flame to get the weight gently rocking (Presto) or jiggling a few times per minute (Mirro), you can go about your business and leave the cooker to do its thing.
I recently launched a thread here about a large Guardian Service PC I picked up for cheap. It's a Presto clone, and I ordered a multiple pressure weight for it to replace its old-school valve. Given the option, the recommended pressure for cooking meats is ten pounds. The Guardian will be great for the next big pork shoulder I prepare. It already did an excellent job on country style pork ribs. I have multiple pressure weights for my Mirros as well (Mirro's one-piece system is superior to Presto's three-piece for this type of weight but none of them are interchangeable across makes -- I found that out the easy way by using plain water and the outdoor grill's side burner while testing a thrift store Mirro find, not knowing a Presto weight would block up a Mirro vent tube -- POW!).
Most things I cook in the PC are done in 15 or 20 minutes, but for those large items that need to cook for 45 minutes or longer, I'm not afraid to walk away. Pressure cookers were designed to save time, not monopolize it.