Isn't it exactly the other way around? The player with the last play is the one who passes second and therefore his end of turn effects won't trigger. So the current implementation reduces the effect of card adventage a bit.
Well, considering that alot of card abilities are disabled after opponent's pass, you are not far from truth, although, exactly the player who has last say controls the length of the round (especially evident in the 1 round - part of the coinflip problem). And can shut down those triggers if he wants to force the opponent to make additional actions or just blowing the ability. The last say doesn't exactly mean last round, last move.
Except, no, the end of a turn does not mean the start of another turn. The best reference of this is MTG, there being an "end step / cleanup phase" where everything occurs and wears off, and an "upkeep / start of turn phase" Where start of turn things trigger and board states are first checked. These are directly and based on linguistic meaning referred to as "start of turn" and "end of turn". I can understand if Gwent chooses to have different trigger priority, but saying things happen at "end of turn" but then not triggering at the end of the turn is completely illogical based on the definition of...well...words.