I haven't had a puncture at all since using this system. Not a single one, ever, and that's with the local riding which is very thorny.
In actual fact, I'm sure the tyres puncture constantly but they just reseal and you don't know anything about it.
Weight wise, there's no advantage, they wheels are a little heavier (probably very little difference it reality as you save weight on the reduced amount of innertube rubber) but the puncture proofing is just so worth it in my opinion. The rear High Roller is worn now, and needs replacing very soon, it's never been off the bike before!
Another advantage is that you can run at lower tyre pressures, without the risk of snakebites. But, being a more, ahem, portly rider, I never drop particularly low anyway but it's nice to have the option when it's very muddy.
As I say though, defeating the fairly is the real advantage as I used to get a puncture at least every other ride and two in one session was far from unusual.
Some people don't like the getto tubeless system, and have trouble with burping (just like as it sounds, under heavy impact air can leak rapidly from the seal) but I've never had any issues with that.
When I finally upgrade the wheels, I will go for "proper" tubeless rims but in the meantime I love my getto system!
Regarding puncture repair, I do have a proper tubeless repair system which I've obviously never used although it does look a bit of a faff. If I ever did rip the sidewall or ended up with a large tear in the tyre, I'd just pop a tube in (and boot if required) out on the trail and then replace it with a new tyre.