How much should a single character be allowed to accomplish in 1 turn?
What you’re looking for is a sweet spot.
On one end of the spectrum, you have: “That guy is able to do way too much before I get another turn.” (Munchkin Quest suffers from this, as described and fixed in my house rules.)
On the other end of the spectrum, you have: “I’m not able to do anything interesting this turn.” (Imagine a game of Monopoly in which you could either roll the dice to move or buy the property you landed on, but not both. The balance would not be appreciably altered, but I suspect the game would suffer nontheless.)
The reason games use interrupt actions — such as attacks of opportunity — is to widen the tolerance of the sweet spot: It allows you to design turns that are long/large enough to maximize the potential for “I can do something fun with my turn” while simultaneously preventing the “why can’t I do anything to stop him from that long sequence of actions?” problem.
The disadvantage of interrupt actions, however, is the complexity which arises from tracking the triggers which allow those interrupts to be used. (Attacks of Opportunity in 3rd Edition gave you a single interrupt action, but had a very lengthy list of possible triggers. Swift actions were later added to the game, giving you a plethora of interrupt actions to choose from; but these almost universally had the trigger of “whenever you want to do it”, which is very easy to keep track of. 4th Edition simplified the list of triggers for Attacks of Opportunity, but drastically increased the number of different interrupt actions in the game and gave most of them different triggering conditions — thus radically increasing the complexity of the game.)
THOUGHT EXPERIMENT: Imagine a 3E-style combat system in which every character gets a single standard action each turn. In addition, they have a single interrupt action which they can use at any time. (For example, to hit someone running past them or trying to run away from them.)
(If you wanted to keep full actions, you could allow them to be taken by any character using their interrupt action on their turn.)
The point is that you don’t define any trigger conditions for those interrupts: You don’t need to keep track of them (or try to avoid doing them). You simply use them whenever you want to and can do whatever you want with them. Theoretically, this would give you the flexibility to respond to actions on the battlefield as you choose, without the difficulty of trying to keep in mind all the possible trigger actions.
Certain effects could vary the number of interrupt actions a character has. For example, a haste spell might simply grant a character an extra interrupt action. (Although on a similar note, you’d probably want to prohibit spellcasting with an interrupt action. An added layer of complexity, but probably necessary for balance. There are almost certainly some other wrinkles to work through if you wanted to use a system like this.)