What are the actual arguments for random encounter over overworld encounters. I personally prefer random, but I'm having trouble articulating why to people.

The three reasons I've got are basically: the corridor design of routes isn't well equipped for roaming Pokemon. It would be more suited if we had full open areas. It makes challenge runs like Nuzlocke unavailable/pointless unless you use something like a randomizer. And it makes "dungeons" like caves or team rocket vases more challenging as random encounters are a test of endurance and make it more difficult to run through an area healthy for every fight.

Are there obvious arguments I'm missing? Is there a more eloquent way to phrase some of the above points?