That and OAs consume your 1&only Reaction, many uses for that reaction coming up frequently could be frustrating...
Wow, sounds like the sort of thing the OP was looking for - care to share?
I already did:
http://www.enworld.org/forum/showthread.php?554094-No-Combat-Rounds
Note that it's not about things in your hands, it's about changing the way combat as a whole works.
Short explanation:
Combat is measured by segments of about 1 second starting at 1.
Initiative is variable, based on the action you're taking. It's really more about when your action resolves - so a normal attack uses d6, an attack with a light or finesse weapon a d4, and a two-handed weapon a d8. (This part was inspired by Mike Mearles rule). To add a little more time between things, after the first turn, you roll dx+4.
Your Turn consists of your Action, potential bonus actions, and reaction.
So if you decide you're making a melee attack with a long sword, you roll a d6 and get a 2 + 4 = 6. So you go on segment 6. Your Turn starts at segment 6, and you can take your action, or a bonus action if you have it. As soon as you complete your Action, you roll again to determine your next segment. You can use your reaction, and appropriate bonus action, between the completion of your action and the start of your next Turn.
In general, the idea is that you are already performing the action, and when you use your action, you are just resolving it. So if you decide you want to attack somebody, then you are attacking, blocking, parrying, etc., and the segment when you get your turn is when you find an opening. So if you want to change your action before your Turn starts, you use your reaction and roll again. If it's your Turn and you want to change your action, then you just roll again.
Think of it this way - you are a cleric and initially move to attack with your mace. You're in the process of that and an ally is heavily wounded. So you react to that (use your reaction) to start to cast a healing spell instead. If it's already your turn, then you just start casting the spell instead (which takes time, represented by the roll).
It sounds far more complicated than it is. It also comes across as very complicated in an example.
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Movement is entirely separated from your Turn. In general, somebody can move 5' in a segment, but really you approach it from the opposite direction. Where do you want to go? A quick estimation from the DM to determine if you can do that walking, or do you have to run? So 6 segments lets you walk about 30'. I'm not going to quibble over 5', and I don't use a grid anyway. Otherwise you have to run.
I have a parry rule - you can use your attacks and/or reaction to parry your opponent. This is just an opposed attack roll. You can also use a reaction to start a Dash, but must use your action to continue to Dash.
So back to movement - if you're 50' away, you need to run (Dash). So you use your reaction to Dash so you're able to close for melee by your action. So we almost never have to consider movement at all, other than that.
Since movement isn't tied to your turn, as soon as you finish your action, you can continue moving - most likely toward whatever you need to, but it can also be away from something. For example, you're 30' away from an ogre that starts running toward you. You can simply start moving away from it, but it's faster, so use your reaction to start to run away. It automatically adds a method to start a chase in the midst of combat.
Players only need to know when their next segment is, and it's always different. You can delay your Action, you just don't get to roll for your next one until you complete it.
Spells work mostly the same - start and end of
their next turn is the same since it always gives them a chance to end something whether their turn is this round or next. Start and end of
your turn is either the same, if it's not something that really matters, or 10 segments if you want to just set a duration. That would be about the equivalent of lasting until the same point in the next round (a little better actually), but not two rounds.
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So since it's basically measuring time, whenever you have a free segment, you can do something minor like sheath a sword. Either you have time to do it, or you don't.
I'd still fix the weirdness of a cleric holding a shield/focus and casting a spell that requires somatic without material to cast the spell using the focus.
And I like the idea of an opportunity attack when picking something up. I already allow an opportunity attack when somebody is standing up - but remember that you can use a reaction to attempt to parry an opportunity attack too. And I have combat maneuvers (mostly for fighters) that take advantage of the reaction as well.
Edit: This is better formatted than the thread:
https://docs.google.com/document/d/12xPT-45PCBvaAJ3FaKI2Tkz2UmMGzoFcCzG0i7BfOss/edit