I've never had boots with as worn an outside layer as yours, maybe because I often use boot covers. So I'm not speaking from experience.
Is it possible you sometimes don't dry out your boots after use? I suppose that might create your issue, but am not sure. Likewise for leaving them in a hot car, in a bag or box or trunk where they can't air out? I tend to baby my boots - I dry out the boots and blades after use, then take them indoors, in a humidity controlled home.
Because the polish is coming off in places, the leather is no longer waterproof, so I think it will be damaged if you don't do anything.
Here is a skate boot taping procedure, from an expert.
https://geppettosskateshop.com/boottaping/However, your polish is in such bad shape that I suspect when you remove the tape, it will take some of the polish with it.
An example of a polish for leather boots is
https://www.amazon.com/Riedell-Figure-Skate-Shoe-Polish/dp/B07BVPNWWXThough that may be more expensive than you need.
Jackson says regular shoe polish works:
http://www.jacksonskates.com/html/care.htmlI was told that if you sand off the old polish, it is common to apply a primer before applying polish, so it adheres longer. I don't know what kind of primer is used.
Likewise, after applying the polish, it is common to apply a "clear coat", so the polish lasts longer, and is easier to clean. But again, I don't know what type of clear coat.
I have no idea what kind of polish or other coatings is commonly used for boots with composite material uppers, such as are used in Edea and other ultralight boots.
Here is someone's video.
https://www.youtube.com/watch?v=FBumxwSAsygOne of her pairs of boots has very worn toes. By the time she is done, the boots almost look new, but not quite.
Notice she suggests cleaning first, letting them completely dry, taping the sole and removing the lace so no polish gets on it, clipping off the places where leather sticks out to create a smoother finish.
Perhaps sanding would eliminate the need to clip, and create an even smoother surface.
But since I haven't done this myself, I can't speak from experience.
BTW I've looked into vinyl repair products for leather, but it looks like your leather is mostly intact, so you probably don't need to go that far.