Is there any point in resetting a level 20 character in multiplayer?

I would say only if they have a ton of negative traits. They continue to get positive traits after reaching level 20 so if you have a good team, stick with them. Besides, nothing is refunded back to you. 

I used respec 4 times until now to experiment.

 It seems that the only benefit of reseting a max character is to get the free respec when you level them again.  Which means it is just saving you on paying for a respec at the cost of having to level all over again.

 It can also be kind of fun to restart a character sometimes, but most likely, you won't do it after you have done it once, because there isn't much of a point and character respecs are common enough or cheap enough that you can change up a spec when you want to.

I think some people like to start from scratch now and then.

wow.. the ignorance in this thread is overwhelming.

resetting a character gives 25 apex rating. no more no less. it doesnt give a respec since you lose all the levels hence all the points (aside from starting points).

its a stupid system and brightly shines a light on just how little thought went into this game since dragon age inquisition does it 1000 times better.

I think you gain some additional apex rating (besides the 25) for leveling the character again. But generally speaking, it's just like @MEGAF1UX said: a stupid option. Don't do it.

@zeroofive no theres not. its 25 FOR THE FLIP. you will get 5 points per match (gold) plus 1 point for every level you get in addition to whatever you get out of boxes. the flip itself is 25 points though. i have heard a rumor (and i seriously consider it nothing more since i have flipped some characters multiple times) that after 5 flips you start getting 26 per flip, but im betting its just somebody being horrible at math and some coincidence being tabulated as fact.