well for fun, those who have big piles of money ha ha
they use in floor radiant heat. Wouldn't that be nice ! I guess cold floors never bothered me because I wear shoes from the time I get out of bed to the time I get back in it. I cannot stand to take even a few steps with bare feet!
the thing about invasive weeds, even if you kill them out with the cardboard, the cardboard will only last for a season or so. Then you have to replace it or the weeds come back. the original plants may be dead but thousands of their seeds are everywhere in the soil and will return so rapidly they can't be controlled. I dug a bunch of invasive grass out of a bed last summer but in no time it was full of seedlings. so many I couldn't keep them out. By putting something more permanet down, it will be several years before having to deal w that again. I did not think of using the indoor outdoor carpet. I think it is relatively cheap to buy new even. Considering it comes in probably 6 or 12 ft lengths and an average pathway would be 2-3 ft wide, you could get several runs for the money.