I used to wax chains back in the 80's when a "narrow" chain was for a 7-speed drive train. It worked really well for road chains...sort of. Couple of points about it:
(1) The technique...paraffin in a pot, directly on a low-medium electric burner. Huge fire hazard, of course. The paraffin has to get hot enough to get thin and runny, so that it does not stick to the sides of the pan. Then you drop in either a new or mostly cleaned up or previously waxed chain that is ready for re-treatment. It should sit on the bottom of the pan long enough to get as hot as the sides of the pan itself...meaning that very little wax will stick to it, too. Then you
carefully agitate the chain. No "shake it in a bottle" here, but it is not needed. The hot wax penetrates the bushings and a little agitation displaces any old lube or wax that was in there, and flushes out any dirt particles that might have worked there way in. You don't need to slow cook these things...the wax has to be hot so I only let them sit for 15 minutes or so. And forget the double boiler...the wax won't get hot enough and all you have is a waxy mess on the outside, nothing on the inside where it is needed. After the chain has been stewed and stirred, you
carefuly remove it with a bent coat hanger and wipe all of the excess wax off of the outside of the chain with a rag. (You are wearing gloves, of course.) The chain will be very hot, and the hot wax will not stick to the outside surfaces, so if you pull it out and wipe it down quickly you'll be left with a clean shiny chain with wax inside the bushings and only a very light residual coat of wax on the outside.
This is way more hassle than any other form of chain lube, so I would do it to 3-4 chains at a time.
(2) The result...on a road bike with 7-speed (old-school, now) chains, this worked great for me. In dry riding conditions (California) it would last around 500 miles before the chain started to squeak. The chain stayed show-room clean and shiny (I always got comments) and when I got flats, which happened all the time with the tires we rode back then, your hands stayed clean when you had to mess with the rear wheel. The freewheel and the derailleur jockey wheels were also always clean and shiny...it was very nice.
(3) The downsides...one rainy ride and the lube job was toast. Not really a big deal if you prepare several chains at once, just pop on a fresh one before the next ride, or hit it with some real lube and ride it dirty until you can put on a clean one.
(4) But...when I made the jump from old-school 7spd to Campy 9-speed back in 2000, I tried it and the results were disappointing. Didn't last long and didn't seem to keep the chain as quiet when it was working. My limited research suggests that maybe as the chains got narrower and lighter, there has been some changes to the design of the internal wear surfaces (less bearing surface, maybe not the full length of the pin in some cases?). This causes the chains to wear out much faster than the old style for starters (I mean, come on...1500-2000 miles on a chain and it's toast???). So whatever changes that gave us lighter 9 and 10 speed drivetrains also seems to have reduced the effectiveness of this technique.
And I was very sad...even as I was snick-snick-snick shifting down the road from the brake levers on a close-range Campy 9 speed cassette...so it was not a total loss.
(5) Now about MTB chains...I never even considered it with the old school chains. A couple of puddles and it was over. I imagine that it would have handled the summer dust and dirt OK, probably better than an oily chain since crud would not stick to the chain and every other drivetrain surface, but since I ride MTB more in the winter, I didn't bother.
Too much detail?