Why? What's wrong with saying "this champion's kit feels awkward and we're going to change some of the mechanics, and because we're not just adjusting numbers we'll cal it a rework"?

My complaint isn't about changing a couple parts of a champion's kit once it proves to be too awkward to play. The problem is that Riot will dramatically change a champion's playstyle or rework everything about a champion without trying to keep that playstyle intact first.

Isn't that what LoL also usually does? There are some cases where a character has been quite fundamentally changed (see: Twitch, Eve, Xerath, Sion), but usually the reason for that is simply that those characters had either a very dysfunctional kit (Sion and Xerath) or a kit that simply had fundamentally broken mechanics (Eve and Twitch with their long-duration invisibility).

League has a lot of champions who have been fundamentally or completely changed when there aren't any massively glaring problems that have proven unbalancable. And Riot also reworks small parts of a champion's kit very often as well. In small amounts neither of these would be a problem, but when Riot is constantly reworking things it means you're constantly losing playstyles. It gets very frustrating when you enjoy parts of the game and they keep getting removed because Riot doesn't want to actually balance them.

Really? A lot of characters that I currently enjoy playing were reworked at one point or another and are much better now than they ever were. Examples:

You mostly listed non-intrusive changes. Evelynn, Gragas, Heimerdinger, Karma, Kassadin, Katarina, Nidalee, Rengar, Sion, Sivir, Skarner, Twitch, Xerath - all of these heroes were completely reworked. Cassiopeia, Ezreal (blue build), Jayce, Katarina (tank build), Kha'Zix, Master Yi (ap), Nunu (ap), Rengar (ap), Tryndamere (ap), Zed (jungle) - all of these heroes had their playstyle dramatically change or had a playstyle removed.

Riot has very deliberately removed a lot of things from the game that many players enjoyed. Sure, a lot of them were really annoying to play against, but Riot could have tried to balance them so that the opponents had more tools to use against these playstyles, or just highlight the weaknesses of these playstyles, but generally Riot just removed or changed them as soon as they became somewhat popular.

The spark that made me finally stop playing League was when Riot decided to rework Kassadin, Gragas, and Nidalee all within a very short time of eachother. These were three of my favorite heroes who had playstyles I really loved, and Riot just culled them from the game. I had lost a lot of playstyles before as well that I also really enjoyed. Riot has a history of removing playstyles from the game and it just got too frustrating knowing that any cool unique nonstandard builds that were discovered would be swiftly culled from the game.