Promo series are a good concept but terribly executed
The ONE really good thing about them is that it creates a level of excitement when going for the next league that is kinda fun.
The thing about them though that makes them so flawed is that the match has so much significance for you but might not for anyone else in your match. This isn't the best analogy but it's essentially a playoff match whereas it could just be a regular season game for your teammates. Thus afk'ing, raging, feeding etc affect you much much more than it does them.
Honestly I think the biggest problem of the system is that "elo" still exists in the background but has no effect on your rank and is only there for matchmaking/LP gain purposes. It doesn't make sense to have a content gold V player playing against silvers to get promo'd into gold. If Riot is going to make the leagues clear cut and defined as they have, then it doesn't make sense to have you play outside of your league. This should also apply for duo queue, which brings me to my next point.
It's also become pretty clear to me that duo queue somehow really messes with their MMR balancing equations and pick order determinations just from seeing LoLNexus in loading screen each match. As a gold IV, I had a bronze 1 duoing with a gold friend get first pick 0_0. The most one-sided games I play in ranked always have a duo on one side or the other.
To sum everything up, I really think that if Leagues are to be as clear cut as Riot is making them, there should, at the least, be NO interleague play, including duo queues. If Riot wants to keep the concept of a promo series, it would make a lot of sense to add a promotion queue if such a thing were viable, at the least for promoting to the next league.
Just my two cents as a person who was at 950 elo in S2 at one point and is now on the way to plat and plays ranked 5's with plat friends. I've seen almost the entire scope of the player base in this game and the concept of a promo series doesn't really make any sense at any level in its current implementation.