The other consideration is speed.
Using a LM method the carpet always needs pre-vacuumed. Not so with TM HWE.
Cleaning 12x12 rooms and moving furniture, a wand is much quicker.
Cleaning stairs HWE is just better hands down.
Dealing with stains, extraction is required.
The above is for residential cleaning.
Respectfully I would argue ALL the points you made...LOL, could stop at just one or two..
1st lm does NOT require (of course depending on the situation) to be prevacced, anymore than HWE, to add moisture to what should have been prevacced is just asking for more problems,
2nd, don't know quite how you got to that conclusion, my machine is 18" wide, moves as freely as a wand and sprays at it goes.
3rd, LM is FAR better at cleaning stairs.
4th, stains? Most are gone immediately, plus for example, you have a tough stain and you get out your spotter and towel? WE simply do that to the whole carpet.