Many years ago I read a great deal about the underlying physics of chains. Essentially there are very high loads within a chain, and it’s important to have lubrication deep inside the pins and rollers. Oil prevents metal on metal contact at the points of pressure, and thus the length of the links is preserved, decreasing wear on the chainring and cassette sprockets. The chain rollers meet the teeth and have little reciprocal movement in relation to the teeth - once contacted, they just sit on the teeth until they rotate off. So there’s little wear associated with the chain mounting and demounting the teeth. The wrap of the chain around the cogs - when the chain is new, and the teeth are new, means that many links carry the load - a good thing. The worry is internal wear on the pins and rollers, which increases the distance between the links, and starts a cycle of increased loading on individuals links on the ‘pull’ side of the cogs, and thus more wear in the chain. External oil does not stop internal wear, and does little good on the outside of the chain other than to attract cr+p, but the problem is getting the right viscosity oil (thick) inside the chain. It needs tori be really thick since the high pressures inside a chain force the lubricant out of the rollers and pins.
That’s the physics. Now possible solutions. For me, the best solution has been Castrol motorcycle wax. This is very low viscosity and migrates into the inside of the chain, where you want it, and thickens by evaporation a few minutes after being drawn into the chain through capillary action. That’s good. For this to happen, the chain needs to be hyperclean, with all the grit removed. You can feel the grit which chains collect by grasping a couple of links and twisting them, feeling and hearing the nasty grinding inside. This grinding paste wears chains quickly, so you want it out. I use chains with a split link, whip them off, clean them in a bath of strong solvent (a big jam jar is excellent) and then dry thoroughly. Wave the chain around a lot when dry, and then more grit drops out. Then reapply to bike, and blast on the chain wax. Leave for a few minutes until the wax thickens, then wipe down the chain. I kid you not, I have had one transmission last over a decade - original chain - by following this regime. I run a lot of bikes, so it’s not just ‘one bike for a decade’ but the longevity stunned me. Good old Shimano - Cleaning only when you twist the chain and feel that grit inside, and getting lubrication where it’s needed (inside the pins and rollers), and not sitting where it should not (on the outside of the chain). The most stupid thing I did recently was to use a thick, expensive chain oil because my Commuting Cannondale was running badly and I was in a hurry. The resulting black filth which then went over everything was a nightmare to clean up. Last time I do that, and back to the chain wax....