The wax that counts is the wax in the chain, not the wax outside of the chain. This is why we quote the miles we do. If I cared about the wax on the outside I would only wax every 1,000 miles or so, or till the wax on the outside is gone. Since I am more concerned about roller wear, I wax every third ride or 120-150 miles which ever comes first. It's like the Jeep engine, if I spray oil on the block and don't put anything in the pan something is going to wear.
I understand the function of the chain lubricant. I was a bike mechanic for a very high end shop in Colorado while I was in college, and my degree is in Metallurgical Engineering and Materials Science. The shop's customers at the time included MTB world champions and Tour de France riders.
Squirt is a wax lubricant suspended in a water solution which came to market about a decade ago. Its easy to apply and you don't have to remove the chain to do it. You put a drop on each roller (don't just stream it onto the chain) and then run the chain about 20-30 rotations and wipe off any excess. It penetrates into the rollers until the water evaporates and then stays put. It tests extremely well in every magazine test, and like I said, you'll have longer intervals between reapplying in dry conditions. It just isn't all that well known. I've finished multiple 100mile MTB races on a single application of it and done well over 500 miles on a road bike on a single application if I don't get caught out in the rain. I've probably gotten 1000 miles from a single application on a road bike, but I've never thought to track it, which is a great endorsement. The stuff just works really well. A .5oz bottle is only $5 on Amazon if you want to try it and a 4oz bottle is only $12 and will probably last you several years.
I'm just suggesting it because I think you'll be really happy with it if you live in a area with dry lubricant is appropriate. I would never recommend changing just before a major ride, but I think you'll really like this product if you try it. I've ridden on alot of different products over the years and this has been the best by far for dry weather.
BTW, the wear issue with the chain on the gears is not due to dirty rollers. Over time, the force you exert on the chain causes it to stretch ever so slightly. As the chain stretches the links space further apart than the teeth in the cogs. This creates wear on the leading edge of the tooth as the roller rides into the cog, ultimately leading to misalignment on shifting. This stretching can be measured with a chain gauge. I believe end of chain life is .75mm of stretch occurs over 12 links. That's an almost imperceptible difference per link, but you can measure it with a gauge.