I'm in favor of keeping Bonus Actions as they are. I can see that you'd be reducing complexity of the turn structure in general by eliminating them, but when describing the individual features that are currently bonus actions as being wrapped into an action all their own, I think complexity will go up, especially when paired with the natural language push of 5e. Depending on how it's worded, you'd either introduce new limitations on what you can do with those new actions, and/or introduce more confusion on what you can do during you action.
Basically, it sounds like he's proposing that something like Cunning Action is actually an action unto itself. A Class Feature Action, if you will. I'd imagine it'd be something like "When you perform a Cunning Action on your turn, you can Dash, Disengage or Hide in addition to X".
"X" is where I see a problem. Either it's very specific - "making an attack or moving" - or it's very broad - "taking another action".
Specific starts limiting what you can do with your special action.
Broad opens up things like "can I use Cunning Action with the Grant Inspiration action, or my Two Weapon Fighting Action?" You could start doubling up on special actions, which would open up balance issues as you have to start looking at the interaction between them now.
A compromise might be "x" being more like a "taking a Standard Action", where Standard Actions defined for everyone outside of their class features. Specific Standard Actions could mentioned, like a "standard melee attack" or a "standard spell casting". However, to me that's just relabeling/re-categorizing and moving the complexity somewhere else.
Of course, what he's talking about is already part of 5E in some places. Look at Green Flame Blade, for example. Making an attack is actually part of the casting of the spell, rather than having casting the spell be a bonus action, which would seem more consistent with the rest of the rules.
Tangentially, you know what'd I'd really like to see? The Attack Action renamed to something else. All attack actions are attacks, but not all attacks are attack actions (i.e., bonus attacks like two weapon fighting, extra attack, flurry of blows, etc.) How about it get renamed to something like the Strike Action. Works well enough for ranged and melee, and you know you're talking about a specific action, not just an attack, which could be part of a different action (especially if we do away with bonus actions.)
But really, keep bonus actions.