Every album I own gets a new plastic inner sleeve after it has been cleaned on the RCM. At that time, if it is in good condition and a "keeper", it also gets a new outer poly cover.
EXCEPTION: If the outer poly cover is better quality (heavy, clean, etc...) or looks as good as new, then sometimes I don't replace it. I ALWAYS replace the inner sleeves, though, after cleaning the LP; no point in putting a cleaned LP into a sleeve that may have dust or grit in it.
If the original paper inner sleeve is plain white and not pristine, then I'll throw it out when the new sleeve goes in. However, if there is printing on the inner sleeve, especially something particular to that LP, I will leave it inside the cover, alongside the new plastic inner sleeve. I think it is part of keeping the LP package more "as original", just like leaving any posters, etc... in place.
I get both inner sleeves and outer covers from a local manufacturer (they also make plastic bags in all sizes and types) who has been making them for many, many years and has a "retail" counter where I can just go and get them by the 100s. Decent quality (non-acidic, etc...) affordable and easy to buy. Almost perfect, for me.
My only complaint is that I really like the extra-thick, heavier covers that are on most Laserdisks I find --presumably the extra thickness and weight of LDs made heavier covers a necessity-- or maybe it's just the way LDs were better quality (and higher-priced) altogether in their day. Unfortunately, the company I buy from doesn't make the covers as heavy; they make regular "LP weight" covers. Not sure if anyone does make those nice heavy ones any more(?). Some of the used LDs I get have dirty poly covers - so dirty that I just won't keep them. The poly covers obviously did their job of keeping the cardboard covers inside in clean and undamaged condition, but it is time to replace them. I have the choice of trying to wash them

, replace them with lighter-weight covers :sigh:, or let them go without covers :nono:. It's frustrating!
I do believe that the poly covers help protect and preserve the cardboard covers inside. Of course, if there is flooding (as others have mentioned experiencing), then the poly covers can hold water in, and cause worse damage. Since I don't expect floods (I live "upstairs" in a building) as much as handling damage, I choose to use the covers.