I've tried it once for a short battle, and players disliked it, especially the spellcaster. After a lengthy discussion, we have zeroed in on the core pros and cons. We had another epic battle, where we used only part of the rule, and it worked great. But first, what is the Speed Factor Initiative variant?
The Initiative Variant
Found on page 270 of the Dungeon Master's Guide is a Combat Option. Speed Factor variant requires everyone to select the Action at the start of the round and roll initiative in secret. In a way, this is similar to how Gloomhaven works: your Action determines your Initiative, and you can't know if you'll be able to execute your plan before the enemy takes their turn.
It was immediately apparent how this rule made players think differently about their turn. It completely removes
Cleric goes after me, he will heal you, I'll go and attack the boss.
and makes you unsure if you'll even be able to help another player before the enemy takes their turn. They had to think about what they wanted to achieve in this round and coordinate accordingly.
Also, as this rule applies to enemies, it motivates players to anticipate the opponent's move and look for opportunities to cancel them.
The round feels like everyone is moving at the same time because the action was selected from the start. And if you know the orc will throw a javelin, it is like he is already staring down at you and aiming while it is still your turn.
While increased randomness can seem like the main problem, I'm still convinced it isn't mainly because it felt like the uncertainty only affected your planning. It didn't determine success.
What eventually showed itself to be detrimental is the locking of an action. Ideally, you would want a turn to feel like a development of the story. A character may start off trying to walk somewhere, discover something, and then use its Action to react to it. It happened in our game, and I allowed the player to use interaction not to force him to wait another turn. If I were to force the player to lock in action at the start of the round, there would be very little room for development as we play.
There were many different options here, but eventually, it became clear that most of them were just ways to mediate the abovementioned downside of the rule. One of them is:
If you want to change your Action, you fall to the end of the initiative track.
But this removes a tactical opportunity to force an opponent into wasting their Action, and it is better to commit to the most punishing form of the rule.
One that I like is the thematic one:
+5 if the spell has only Verbal components.
-5 if it has Material Components that aren't replaced by spellcasting focus while casting.
The good homebrew rule
We played a huge battle with the following variant, and it was great.
A big group of enemies will have a passive initiative count (10 + Dex).
Players reroll their initiative every round.
And that is it. As you roll the initiative you learn if you'll take your turn before the enemy or after. It felt nice to count down the initiative track "20, 19, 18..." as players glanced at each other, it felt like the turn timer is moving.
So we end up not using any Action Locking, you decide what to do when your turn comes. We did use a few more rules for that huge battle below:
Injury system to track HP of low-level monsters.
Cleaving through creatures.
Impredictibility of turn orders is the favourable element, as it incentives a more immersive way of thinking. But being unable to choose an action on the fly takes players out of the moment.