I'm just not seeing how side-based initiative actually improves 1) player engagement or 2) player strategy (or the other goals sprinkled though the thread, such as speed of combat and "realism".) Especially when bolting it onto a system like 5E - the game the OP is thinking of modifying -where individual initiative is assumed in the rules.
I am not addressing (in this thread, so far) how it would work with 5E. This is TTRPGs General, right? As we're all aware, spell and effect durations in 5E are written with its individual initiative system in mind, so implementing group initiative in that game necessitates much broader changes.
If you don't see it, you don't see it, I guess.
Whether side based initiative is
faster... I would tend to say that the fastest system is just going around the table. One I've seen implemented is to roll side-based initiative at the start of combat, then just go around the table in the same order all fight. My system definitely involves some kibbitzing and debating at times, but it's generally all in one discussion on any given round, rather than there being debates and discussion about optimal strategy on each PC's turn, as sometimes happens with sequential individual initiative, at least with some groups.
Whether it's more
realistic... I suppose it kind of depends what you're trying to simulate. If you want to give some fog of war and confusion and simulate some of the lack of perfect information you see in real combat, and in some fiction, requiring action declarations at the start of the round can definitely give you some of that.
I don't think letting my players coordinate their turns and take them in whatever order they like 5 rounds out of 6 is particularly realistic, but I think it's generally in service to fun and to letting their characters act in a heroic and coordinated manner, with good teamwork, and most of the time it runs pretty fast.
In addition to the mixed version in The Fantasy Trip, I mentioned I'm also playing Mork Borg, which is very rules light and used group/side initiative. And that worked fine. Largely in part because characters and NPCs don't have more than a couple abilities the player or DM needs to track, not a lot of enemies at once, and solo enemies scale well.
Generally this is true of the 5 Torches Deep & B/X mashup I run, as well. Though I do sometimes have a lot of enemies in play.
Speaking of Mork Borg, that reminds me of something I almost brought up in my prior post. Making the players roll defense instead of rolling attacks against them is another great way to help maintain player attention/engagement.
