Lanefan
Victoria Rules
Shuffling and deealing cards each round can't possibly be any less fiddly than rolling dice.I don't really like this, for many reasons. It's fiddly, wastes time, warps balance, wastes actions and overall it feels like a pet project that will only waste design time with important opportunity costs for the worse of the game.
If you don't like cyclic initiative, there is a simpler way to keep stuff running. Get a deck of cards running from 1 to 50. Whenever it's time for combat shuffle and give each player two cards + Dex bonus (minimum 1) then the DM draws one card for each monster + the best Dex bonus in the group (+1 for any legendary actions). DM puts her lowest card and declares which monster acts in that slot. Players with a lower card can show it and get their action or movement before that monster. Monster gets their turn, DM shows another card and players with a lower card can get an action or movement before that monster. And so on until all monsters get a turn, then any residual players get their turn. Shuffle and repeat. As long as players have actions or movement they can keep intervening with their initiative cards. Once they are out of them they discard all of their cards.
This way players have to keep attention as they don't know when they get to intervene, and they aren't pressured to use their bonus action as it could still be useful later.

Also, at first glance this seems to give a significant advantage to the PCs, as they are always reacting to the opponents rather than proacting. Ideally in any random-order system nobody knows who will act next, but here when the DM lays a card down and says "the ogre acts on this count" the PCs who would otherwise act before it have information (the ogre acts before any of the orcs) that they should not, which will influence their decision-making. The opponents don't get the benefit of this same advance knowledge.
At least with true cyclic initiative everybody has the same knowledge, that being the turn order. Randomizing initiatives is intended to remove this.
Lanefan