My takeaways from this:
1. Bonus Actions, as a whole, are taking the heat from Off-hand Attacks (and perhaps other bonus action attacks) being a fundamentally flawed mechanic. No, spending a Bonus Action to Dodge or Dash isn't a problem, nor is the mechanical freedom to mix and match Bonus Actions with various Actions from different classes, races, and feats. It's specifically the Off-hand Attack that is really causing problems, due to being generally weak and getting in the way of other cool stuff.
Consider this; Dragonborn Barbarians can use their Bonus Action to enter a Rage and their Action to use their Breath Weapon. A one-round plan that is thematically appropriate and unique to the Dragonborn Barbarian. In order to replicate this without Bonus Actions, you would instead need to create a Special Action exclusive to Dragonborn Barbarians, and one for every other Dragonborn+(sub)class combination, so that they could use their breath weapon and their class-defining Bonus Action. That's just way too fiddly, and requires tons of redundant text and space.
2. This initiative system is backwards.
Firstly, because of it's design, you pick something and roll, then do the stuff. It should be the other way around: You do the stuff, then roll for it as a recharge on the next round. That prevents wasted actions and the like, while still enforcing consequence, and even gives the added benefit of trying to set up for faster and bigger actions in the next round.
Secondly, Rogues and Monks and Rangers shouldn't be the "slow" classes. They are the "fast" classes, which is why they get the fun bonus actions in the first place.
Even with changes though, I don't see myself using it. It's just too, for lack of a better term, "Video Gamey" , requiring an unnecessarily high amount of math variables. And feels like it belongs in the back end of some code as a hidden complexity for the uber-nerds to suss out after hours of reverse engineering for high end play.