What's the benefit of tubeless (never used them myself so I'm in complete ignorance) ?
No pinch-flats, so you can use low pressure. An advantage for MTBing.
Is it just as easy to fix a puncture as just throwing in a new tube is with ordinary tyres ?
I think you can fit an ordinary tube if sealant doesn't work or whatever.
If you don't fit a new tube, you've got the interesting problem of trying to get a seal with a mini-pump. You can use CO2 - one cartridge to get the tyre seated, and one to get the pressure, or CO2 to seat and a pump to top up.
If you do fit a tube, why not use an ordinary tyre?
You can use a sealant in those if you want.
So you end up with more complicated puncture repair, in return for which you can run at low pressures that would otherwise put you at risk of pinch flats. Nobody uses pressures that low on the road (deliberately), so tubeless have no advantages.