Hello! First of all, let me say I'm glad you've decided to change "The Crowd Chose You". I sure the majority of the pvp community agrees is not the best way to determine the winner of those long arena matches. Unfortunately, I don't think the proposed "Dampening" effect is better substitution. The stacking healing reduction which will begin to increase at the 10 minute mark
will make it so hard for healers to do their job that players will not even need to cc them in order to score a kill. This way,it will not require skill and awareness from the players, just
"tunnel vision" damage pumping until something dies.

I propose that at the 10 minute mark and every 30 seconds afterwards everyone gets a buff
which increases damage and healing done by 10%. Now at first this might look as the damage buff will offset the healing but at high values(somewhere around the 15 minute mark) damage will be so much that shorter cc chains on the healer will be required to score a kill. Eventually even a single silence or stun should be enough.

I believe that this way is more fair for both roles to shine, e.g. the healer of one team is really good at avoiding cc but they can't kill anyone from opposing team for some reason. After buff comes the healer's ability to avoid cc will come in handy as damage will be so high that you just need to healer non stop.

Damage dealers ,on the other hand, who only have a small window to score a kill(either because of small cc chain for opposing healer or small window of being able to deal damage),
as the buff stacks, will have higher and higher chance to win, granted they are able to survive incoming damage.

In case that the arena match stretches to the 20 minute mark(which I believe is impossible with the proposed change), the match should be ended and both teams should lose rating.
Deciding a random winner in the end based on some other hidden or not criteria is just plainly unfair.