But I haven't heard a good scientific explanation of why that would be. I don't see skin oils breaking down plastic line, or the water in the creeks.
Ok, here goes. Disclaimer: I don't know this to be true about fly lines specifically. But it is true for most plastics designed for the outdoors, and fly lines are plastic. It's the same principle which works on your car's finish (the paint/clearcoat is a plastic) as well as the headlight assemblies and so forth, plus plastic beverage containers, and any outdoor plastics, really. Your waders, as well.
Ok, so the enemy of plastics is UV light. Without any protection, plastics break down in UV very quickly. As in, minutes.
Now, when they make the plastic, the surface layer is impregnated with UV inhibitors. These don't actually block the light, but rather, chemically inhibit the chemical reaction which breaks down the plastic.
Now, dirt is very abrasive, and tends to wear away the top layer of the plastic, plus roughen the surface, which leads to more dirt, which leads to more abrasion. After those UV inhibitors on the surface are gone, it's game over. Your line will crack. Your clearcoat on your car's paint will fail (fade then peel). Your headlights will fog over. Your tippet will get kinda whitish and become more brittle. And your gatorade bottle will release all sorts of plastic contaminants into your drink (and eventually fail completely). Your waders will first leak and then just begin falling apart.
Cleaning a new line in good condition will keep that surface smooth, which will allow less dirt to attach, which will prolong it's life. Even better if the cleaner applies some sort of a wax, which prevents dirt and chemicals from sticking, and for any that does stick, becomes a sacrificial layer (you abrade the wax instead of the plastic underneath).
Want to prolong the life of the clearcoat on your car? Keep the car clean and wax/seal it periodically with the longest lasting sealant you can find. Sounds strange because it's UV that does the damage and you aren't actually blocking it. But the the UV inhibitors are in the plastic surface itself, and your job is to protect that surface. A surface coating is added to virtually all outdoor plastics.
The same applies to your fly line.
And note that maintenance will merely prevent PREMATURE failure. Eventually those inhibitors in the plastic, which are acting chemically, simply run out. Fly lines need replaced, cars need resprayed, headlights begin needing polished every few months, and waders weaken and fail. And you shouldn't drink that case of Gatorade that sat out in the sun for a year.