Downfalls of on-screen encounters:
-The need for monster graphics. It can look really boring/strange and the same otherwise. There's only so many monsters and spriting them is rather hard. (requires heavy sprite knowledge and time to make graphics).
- The maps need to be designed to keep avoidance in mind. (Sometimes maps can get ugly or lose direction when you constantly have to keep this gameplay element in mind.)
- Encounters are on screen but you can't avoid them. You MUST fight them because developer didn't consider making it possible to avoid them.
- When grinding you have to constantly switch screens once all the encounters are fought or even worse the inability to grind when encounters disappear forever.
- When running away from battle the encounter doesn't give you enough time to escape the on-screen trigger, forcing you to run away from the battle several times. (can be extremely annoying especially if it's hard to escape.)
- Swarmed by several on-screen triggers at once, forcing player to have to engage in one battle after the next with no time to access the menu in-between.
I don't think it's necessary to create a sprite for every monster ( as you said, it would be very hard ). I like how this problem has been solved in Eternal Eden: every secondary encounter has a smoke sprite ( maybe the smoke is not the best choice, but you can change it with a shadowy figure or stuff that's already in the RTP ).
For the avoidance, to which I agree, there's a script from Yanfly ( or Formar0153, now I don't remember ) that allows you to limit an event movement to a certain region. So you can forbid those events to go in small places where they can become unavoidable.
For the grinding, if I'm getting correctly your though, it depends from how the programmer manage exp points. I''d probably give 5 to 10 times more exp from a set battle than I would on a random battle. So you take less time to grind and, at the same time, you still need to fight a lot in order to reach a higher level. Plus you forbid the player to get too powerful too early in the game.
For the triggers, I agree with you. But there must be a way for the player to escape from the sprite ( this will probably be one of my biggest difficulties: find a solution for this problem

)