Nup, thays not it either.
As the system stands, youd have to forgo an action on your turn and set a trigger, such as "i attack the first person to come into range of me". And then if that happens, they can use their reaction as well to make that attack.
However if no one approaches that pc, then their action is wasted.
I dont know anyone that often uses reactions due to the sacrifice of their action on their turn and the chance that it may be wasted anyway.
So there might be a few situations where an expanded reactions list might cone into play.
For example if a pc is the target of an attack, they may be able to use their reaction to move 5' in any direction. Away, behind an obstacle, towards the target, etc.
Or a player may choose to grapple or shove if an enemy moves out of their threat range.
Here are some wip ideas:
When charged or attacked at range
Move 5 feet
Drop prone
When attacked
Grapple
When triggered
Use a readied action
When leaving threat range
Opportunity attack
Grapple
So you are wanting to expand the list of triggers to include common combat activities *and* expand the list of "allowed as reactions" to the point that, it seems, practically speaking on most if not every turn in a significant combat someone is likely to be able to use a reaction *without* special preparation or planning?
One of the things i like about combat in 5e is that planning and tactics matter. Each turn you do not just get handed to you useful actions, bonus action and reactions all as a matter of course.
You have to plan and execute to frequently be able to be able to use all of these in a round/turn *or* an enemy has to make a decision to give up an opening like say exposing themselves to an OA.
So, this degree of expansion to allow reactions basically when attacked by range, melee or charge goes to that planning, tactic, setup and says "dont bother, you will get a reaction each turn mostly anyway."
So not a fan.
Also, it really fosters even stronger rhe dogpile mentality. It makes "everybody hit one guy" even better than it is now because the target only gets one reaction. Spreading out attacks across multiple targets allows more reactions and would be bad under this paradigm.
Now, maybe one sees that as great tactics or what not, but to me that really cuts into many style/setting goals. Are you trying to emulate mmo beat downs or fights like we see in fantasy novels and films where often each lead character is in battle with one or more enemies in a big fight?
From a PC perspective, would the fights be more fun or less fun if the bad guys, intelligent ones, all piled damage on one guy until they went down, then shifted to another etc in paet because that prevented a lot of "extra reaction attacks"?
Are those fun goals? That would be what a pretty much "take reaction when attacked" house rule rewards.
All that said, this might well help for certain styles of play and groups to achieve a playstyle they like. It will certainly increase the number of off-turn actions and maybe that per turn action density is desirable - at leadt until they see how it impacts their ability to stay up due to enemies getting all their reactions too.
But for me it takes a plan/tactics gain and just hands it out and seems to really ramp up the actions per round in a very slanted way.
At the very least, you should considet giving spell casters the ability to throw one action cast spells as reactions to typical combat events just like you allow shoves or grapples and seriously look at the triggers of "reaction spells" to expand them too. As is this seems rather one sided giving options to get non-spell based full actions as reactions but not spells.
I mean, what spell based options should i get for an enemy grsppling me? How about a reaction dimension door?