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Both random encounters and overworld encounters have their own charm and mechanics the game could play around with.
The random encounters are fun if you want to go into an area completely blind, not knowing what you can encounter. Not only that, but it fits the aesthetic of Pokemon in general if you ask me. Yes it is outdated and I agree that it could be replaced with the overworld encounter system as it does provide the necessary immersion the player desires, especially since it makes the world look a lot less alive, a lot less messy in comparison to when there are 8 individual Pokemon cluttered all over your screen, but still kind of ruins the immersion you can have.
Now, the overworld encounters also have their own charm and upsides as well as downsides, the biggest charm is outright knowing what you want to go for, giving you the options to try and evade the Pokemon you do not want to encounter. Not only that, but it brings a lot of life to the world and really solidifies the experience you can have. However, the problem I see with this is that as it stands right now and has been demonstrated with Pokemon LGPE, the overworld encounter mechanics leave much to be desired, what I am talking about is having to wait a lot. In the previous games, they had mechanisms to chain an encounter to get a special version of a specific Pokemon you are hunting for, it is still the same with LGPE of course, but having to wait for another Pokemon you are looking for to spawn gets quite tedious, in that aspect I've experienced more joy with the random encounter system and using DexNav/Suction Cups + Fishing/SOS Chaining than I had with the Catch Combo system.
So my final verdict, both got their ups and downs and are good as they are.
I really couldn't pick a side.
They can both be improved upon to really make them stand out as they both have plenty of potential for delivering a great Pokemon experience.