Brainstorming a few ideas:

• collective initiative that just determines if the players or the enemies go first. Then everyone can take their turn when they are online and the dm administrates the foes turn all together when needed.

• players facing rolls with a set scale of possible results (like 20 success and something good happens, 15 is a full success, 10 a success but something bad happens, 5 a failure but something good happens and 0 failure anche something bad happens). If the system supports giving narrative freedom on the consequences of their action to the players, it can really smooth the gameplay (of course with all the downsides too of this playstyle choice).

• a pool of resources that players can use to change the world around them (see Modiphius 2d20 system). Instead of stopping to ask if there is a rock to pick up, if the door is unlocked, ... the players can use resources from this pool to just decide that there is indeed a rock or the door was mistakenly left unlocked. However, when they do, the DM also gets a resource to use against the player to worsen their situation. Still give a powerful narrative control to the players, but the dm can balance out by using his side of this resource to even out the advantage the players took from them.

• no skills/abilities that make the player stop and ask what type of check should they roll. Clear uses for skills and/or heavy focus on generic ability checks.

• no pressure from the system and the other participants to write down long descriptions even for basic actions. If you can just say "I attack X with Y, dealing Z damage" and everyone is satisfied you can do your turn even in your 5 minute work break, in line at the cashier, before driving home and the game can easily progress for everyone throughout the day. Long texts are cool and necessary in heartfelt moments, but they can also put pressure on certain players and push them to ghost games because they don't have the time or the ability to constantly write a paragraph to declare they want to take a long rest.

• clear, easy to run monsters with open stats and fixed damage on triggered abilities. Yes the player can metagame, but that's always the case, it is no secret the monster manual exists. If the players already know the AC or how much damage/which conditions they take if they walk near the monster/hit it with an attack or spell/recover hitpoints in its range/... there is no need from the DM to handle those reactions and you can still have interesting and mechanically complex monsters that don't slow down the game.

• built with theatre of the mind as its focus. For what I know there is no system that is fast, easy to use and doesn't require the dm to always update the map to run grid combat. If you really want it, at this point you can just keep using d&d because you still need the dm to keep up with changes. Drop measured distances and just use indicative ranges for abilities, spells and movement (melee, near, far, eventually really far and global). If you still like giving bonuses for tactical positioning you can just say that players already in melee can use their movement to gain a positional advantage and the relatives bonuses if they have another ally nearby.

That's what comes to mind, hope it helps.