I can tolerate random encounters if they let me flee battles easily or they let me activate an item that temporarily lowers encounter rate, like in Pokémon.
Pokémon is really the only franchise that actually execute the idea of random encounters perfectly. An encounter doesn't only mean you're gonna get XP out of it, you can find a pokemon you really like and bam, new party members, or at least grinding actively makes your existing party members better through EVs. It only becomes a pain when you already have your finalized team with everyone at high levels, but that's like at the end of the game pretty much.
Sadly other games just make the encounters unbearable from how frequent they are, I dropped Breath of Fire IV because of that.
One thing about Pokemon that I don't really see people talk about is how it is also smart enough to have both random encounters AND on-field encounters. I can't think of another franchise that has the mix of the two. The overworld trainer battles have smarter battle AI, give more XP and many of can be maneuvered around. Random encounters don't feel like such a boon because on top of generally lower encounter rates compared to a lot of RPGs that people consider problematic, there is the ability to turn them off as well as the ability to potentially capture a new party member, like you said. It obviously also helps that outside of caves and water, random encounters only occur in tall grass so if you don't have any repels and don't want to get into encounters you can just avoid tall grass as much as you can. Thanks to most XP coming from overworld trainer battles that feel like more of an engaging spectacle you rarely ever feel punished for rushing past a lot of the random ones. Once they gave you the option to rebattle powered up versions of trainers you already beat in gen 3 you never even needed to grind random encounters if the tedium didn't interest you. It's really quite something how elegant the way those games are setup!
I wonder how other games could try to implement hybrid systems that would allow for some of the positives of random encounters without them feeling as obnoxious to people with less tolerance for the mechanic. Maybe its a game where you are being pursued by a hostile enemy force, with those enemies (let's say knights from an enemy army) are visible on the overworld/town map when present, while monsters are still random encounters. The trick would be trying to find a way where both systems feel relevant in some way.
Maybe its a game like SaGa where monsters are allowed to be party members and you can have your party monster eat or absorb monster essence to change their capabilities on battle, or you could just have a more straightforward capture system like Pokemon. Then - since in this hypothetical game we're a party of primarily humans in a fantasy setting - the enemy knights or whatever the overworld enemies end up being could drop higher gold counts on account of being actual people who would naturally have more on hand as well as chances to directly drop gear.
The game could even just separate the two encounter types by how they impact your economy. Monsters would drop materials for crafting and maybe give more XP on average whilst overworld encounters would again drop more money and have the chance for direct gear drops. Maybe weapons can be augmented with crafting materials so you'd ideally be defeating overworld enemies to get gear and then monsters to augment the gear with different attributes (think Final Fantasy X's gear system).
Basically, I'm just tryna lay out that there is a lot of room for exploration there, as difficult as balancing that economy would probably be for any designer daring enough to try. I really appreciate this comment because until now I never really appreciated why Pokemon was able to feel less tedious despite hypothetically introducing far more tedium into its encounter system. Despite having up to 6 separate party members that can only level up 1 at a time or have to level up slower via shared XP even the older pre-XP Share games are rarely thrown onto lists of the most tedious RPGs.
