Are tubeless tyres an upgrade from tubed tyres, or just different?
What if the puncture is not adequately sealed by the sealant? Can I patch a tubeless tyre in a permanent way with a glue-type patch? A permanent repair without a slow leak for inner tubes is easiest when you always carry one spare tube so that you let the glue dry before using the newly patched tube. Unless some major form of technology breakthrough has occurred of which I'm not aware, if a tubeless tyre can be permanently repaired at all (which I suspect won't be the case because of the sealant &quot;slime&quot;), you should always carry one spare tubeless tire with you to let the patch glue dry. Carrying a spare tire takes more space and weight than carrying a spare tube.

No, if the sealant and specific plugs (mentioned in Diado's answer, the same ones that are used for automobiles and motorbikes) fail to seal the hole, but the hole is not extreme, you can just swallow your pride, insert your spare tube, and carry on riding. If the hole is large, you will need a tyre boot in the exactly same way you would need it for a normal inner tube tyre. Then at home, after a good clean, you can indeed use a tube patch or one of the larger tyre-specific one. If the hole required a boot, it may also require some sewing. and then covering by a polyurethane glue and a patch.

What if the cords of the tire are damaged? With a tube-type tire, there is no sealant &quot;slime&quot; so I am certain that an adhesive tire boot will stick to the inside of the tire. However, with tubeless tires, the sealant might make it more difficult to ensure the adhesive tire boot stays in the intended place.

That is unlikely. Quite the opposite, it will make it stick. Or at least be neutral.

So, why should I care about tubeless tires? I see them as a non-repairable solution that harms the use of emergency tire boots and at the same time encourages the rider to cause rim damage.

It is repairable (I repaired several punctures myself) way that makes better riding properties especially off-road (lower pressures) and reduces the number of punctures you have to deal with (no pinched tubes, small thorns are plugged). Small unsealable holes can be plugged without taking the tyre or indeed the wheel off the bike.
Any potential rim damage is the responsibility of each rider, their selection of the tyre pressure and their choice of their riding style.

The user error requires the presence of three conditions: (1) the tire must have a narrow cross section

Pinch flats can also happen with MTBs.

(2) the tire must be underinflated

Low pressures are selected for good riding properties and it is impossible to perform well in certain off-road events (cyclocross, cross-country) with such high pressures an inner tube would require. The other option is a tubular, but that is even more hassle.

(3) the rider must go over a bump at too high speed.

Stones and roots may be hidden by mud, leaves or appear suddenly behind a corner on a trail. Sometimes they cannot be avoided even on a maintained course, less so in unmaintained trails.