This is exactly what I believe Mearls is going for. You're not "just" dropping bonus actions as the OP suggests.
Note that not much would really be added, as most abilities already have additional "ad-hoc" text to specify how the bonus action can be used. You have, however, pared down the action economy and any confusion on "do I get a bonus action?" I too have had players assume a bonus action is something they get each round and have to find something to spend it on.
I do think some over-arching codification could still be beneficial, though - i.e., special actions vs. regular actions - especially to help alleviate stacking concerns.
The rules already state you can only take one action a round. So the simplest solution would be to, first indicate those things which considered regular actions, simply by renaming the "Actions in Combat" section to "Regular Actions in Combat". Then it's just a matter of clarifying that things which are currently bonus actions are simply actions.
For example:
Patient Defense
When you take this action, you can spend 1 ki point to take the Dodge action in addition to any other regular action on your turn.
Flurry of Blows
When you take this action, you spend 1 ki point to make two unarmed strikes in addition to taking the Attack action on your turn.
The same would go for Bardic Inspiration, Cunning Action, Rage, etc. Since these are now clearly indicated as actions, there's no concern about stacking.
There are only two catches I see with this approach: Two-weapon fighting and "swift" spells.
This might be where explicitly declaring "Special Actions" would help. So, replace the "Bonus Actions" section in the Combat chapter with this:
Special Actions
Various class features, spells, and other abilities let you take an action on your turn, called a special action, which is not considered a regular combat action. These often allow the character to do something in addition to a regular action. The Cunning Action feature, for example, allows a rogue to Dash, Disengage, or Hide in addition to a regular action on your turn. Since you can take only one action on your turn, so you must choose which special action to use when you have more than one available.
"Swift" spells would still be spelled out (no pun intended) separately, as Li Sheron does above, but now as a special action. I might add the following to the Magic chapter of the game:
Casting a Swift spell
Special action. When you use the Cast a Spell regular action using a spell with the swift property, you may also cast a cantrip or take any other regular action.
Two-weapon fighting is something else, though. It's the only bonus action I can think of that's not an actual class ability or spells. Anyone can do it if they want.
TWF has always been a quirky mechanic ever since 1E. It certainly lines up certain fantasy/swashbuckling archetypes, but as a free extra weapon attack, is difficult to balance. This edition's solution to balance it is to make it require a bonus action, limiting weapon type, and losing the ability score damage. That last drawback is easily overcome with the right class option or feat.
So the bonus action is the biggest trade-off for attacking with an off-hand weapon. It's probably the most "kludgey" part of bonus actions, really. If we dump bonus actions, we either have to give "normal" TWF another trade-off, or make it clear it's a special action not included in "regular" actions (if stacking of TWF and other former bonus actions are still a concern.)
If we've already defined special actions, then we just need that indicator added to the Two Weapon Fighting description in the Combat section:
Two-Weapon Fighting
Special action. When you're holding a light melee weapon in one hand, you can take the Attack action for that weapon, and you can make an additional attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of this additional attack, unless that modifier is negative. If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.
For class features which give TWF as a fighting style, no changes are needed.
In fact, a lot of redundancy can then be eliminated if special actions have been specifically defined as something different than regular actions. Going back to the monk:
Patient Defense
Special action. You can spend 1 ki point to take the Dodge action in addition to any other regular action on your turn.