Cyclical was a good innovation. Speeds up combat, which is always a bonus.
No, cyclic initiative does not speed up combat. What it does is make the whole business of who goes when highly ordered. If the DM was the type to have a lot of issues with chaos in the player/DM communication, this will probably result in a net speed boost for combat. If the DM wasn't, it will not, and will probably be slower than whatever the DM was doing before.
Moreover, cyclic initiative does the least damage to combat speed when it is least needed--i.e. with relatively few players. That is, if you have 3 or 4 players and are goofing around, applying the order of cyclic initiative may help, but it will not scale well when your two friends from out of town sit in on the session. Whereas side initiative systems tend to take more upfront work for the DM to master, but then scale very well. (And it's all well and good to say nonsense like, "people shouldn't be playing with more than N players, anyway, so why design for more?" The design team of the game doesn't have that option--not to mention, it's incredibly shallow and lazy design to do that.)
Most of all, though, I can't believe all the same people complaining about "tactical elements" in the game and then turning around and thinking that cyclic initiative is so wonderful. Where do people think those tactical elements were anchored in the first place?

The speed problem from cyclic initiative itself is minor compared to all the secondary effects that then need to get addressed, and the systems that spring up around those.