Don’t know what edition you are referencing
My guess: The ones that you find difficult to read due to "mixed notes for one hand between the staves" are Urtext editions. I believe this is how music was written in the time of Beethoven.
My guess is that your guess is correct. The long term trend has been to make the score more of a set of instructions as to what buttons to push and less of a picture of the music itself. An extreme example of the early notation as a picture of the music rather than as a set of instructions would be Bach writing the Art of the Fugue with each line on a separate staff (and with its own clef) and counting on the organist or keyboard player to digest it all and figure out how to distribute the voices between hands. In Beethoven's manuscripts the notes mostly just go where they go without regard to what you have to do to play them. Later editions tried to make reading easier by assigning the upper staff to right hand and lower staff to left, at least as much as possible.
Topic: Why has piano notation recently moved to hands being split across staves? 