Personally, I think the question is not just changing the odds of getting a shiny, but also the mechanism behind it. Part of the mechanism needs to be chance based, as that gives that adrenaline rush feeling when you actually do get a shiny (for comparison, I'd say the guaranteed shiny gyarados at the lake of rage feels underwhelming). Making it entirely chance based with 1 in 8192 on the other hand makes it too luck driven, with many never encountering shinies during a full playthrough, while some might encounter multiple. Additionally, this greatly inhibits hunting a specific shiny.
Most games have additional mechanisms. The first one is the shiny charm, which increase the base odds of a shiny per encounter. The bar for getting one is set high, having to complete the regional or national pokedex, which given the boost in shiny rate is fair. But this is a high time investment to get an overall boost.
Another method, chaining, focuses on increased odds by maintaining a chain of encounters of a specific pokemon. The way chaining has been implemented varies per game (I am not known with how it works exactly in Sword and Shield). The benefit is that it does only affect the pokemon you are chaining at that specific time (again, I think Sword and Shield might do this differently, perhaps making it too easy).
Then there is the Masuda method for breeding. The benefit of this allows the highest odds of ensuring high IV's and natures.
Ultra Sun and Ultra Moon introduced a mechanic that involves travelling as far as possible in a wormhole minigame (I guess it could be compared to an extravagant flappy duck minigame), which then increases your shiny odds. My experiences were that this made it waaaaay too easy to get shinies, devaluing a whole set of shinies as a result (shiny altaria feels very cheap for me right now).
I'd like to focus on two specific suggestions I have when it comes to shiny hunting. First, having a mechanism akin to the old gold/silver/crystal games, where you can dramatically increase odds if you find the correct pair of parents. Of course I think this went a bit too far in the gen 2 games, but the idea that one can have hidden values (note, it does NOT need to be tied to IV's) corresponding to the shiny chance appeals to me. That way, instead of solely relying on chance, one can make progress in getting a shiny. It would be nice to have a system similar to how one can breed 5-6 IV pokemon with specific natures over multiple steps, but for shinies. The reduction in chance will be replaced by the effort needed of going from one step to the next.
Next, I'd like to talk about legendaries and soft-resetting. In my opinion (and I admit this is extremely subjective) soft-resetting feels kind of an unnatural way of playing a game. There are instances however where people can run away from an encounter and still be able to start it again (for instance the latios encounter in alpha sapphire). This run-away strategy removes the endless restarting of the game. I'd prefer if games allowed this for all legendaries. Perhaps this makes the time between encounters way too short for some people, but having to watch a start up screen between every encounter does not really feel productive to me. I did get a shiny Latios via the run-away strategy and must say it felt extremely rewarding (perhaps more so than the first shiny I got by chance, a shiny spheal, because of the amount of effort I put in).
So in conclusion, I can not answer the poll: I believe that the combination of effort and luck are central and should be balanced.