During the playtest, there was a Charge action that all characters could use. What it allowed was that as an action, you could move up to half your speed, and attack any adjacent creature when you finished moving. This effectivley allowed you to have a movement of 1.5 times your normal movement rate, in exchange for losing extra attack etc.
Besides trying to figure out what half of 25" is, and being open to the odd debate about if it counted as an attack action for extra attack or not, it didn't negatively impact our game much. We did not add any bonus to hit, or a penalty to AC, but if worrying about those modifiers is not a concern, or if you enjoy that sort of thing, I think a +1 in either direction would be fine.
Compared to the feat, there is still a reason to take the feat since you gain an extra 10-15 feet of movement, and can also shove and not only attack. However, I would bump up the feat to also give a +1 to str to compensate for the new houserule.
The language is unclear
The intent may have been that you must wait for your Action to complete before utilizing your Bonus Action.
Jeremy Crawford had previously tweeted that Bonus Action timing was completely up to the player regardless of the trigger requirement. While this gave a lot of freedom of choice, it wasn't really fully in tune with the written rules on Bonus Action timing (emphasis mine).
You choose when to take a bonus action during your turn, unless the bonus action's timing is specified...
However, that tweet has been updated after realizing his mistake.
Clarification about bonus actions: if a feature says you can do X as a bonus action if you do Y, you must do Y before you can do X. For Shield Master, that means the bonus action must come after the Attack action. You decide when it happens afterward that turn.
He further clarified with this tweet
No general rule allows you to insert a bonus action between attacks in a single action. You can interrupt a multiple-attack action with a bonus action/reaction only if the trigger of the bonus action/reaction is an attack, rather than the action.
But that clarification was...wait for it...further clarified again:
"My tweet below was addressing bonus actions and reactions that have triggers. A bonus action that has no trigger—such as Cunning Action and the misty step spell—can take place whenever you want on your turn (PH, 189)
The RAW and the Crawford
It seems clear that Crawford's intent for Bonus Action triggers is that there is a requirement for the triggering Action to fully complete before you can take the Bonus Action. If you go by this, then you are not able to take your Bonus Action inside of (interrupting) your Attack Action.
A question of wording
However, as stated above, GWM is not triggered by the completion of an Action, but by the killing of or reducing an enemy to 0 HP. Given that the trigger is not based on the Attack Action but on the result of a hit combined with the rule on choosing when to take a bonus action during your turn, then it seems possible to interrupt your Action.
Which way to go?
I understand what Crawford is saying in that Actions are complete events that can not be interrupted...except by movement. His clarification that you can't interrupt one action (Attack) with another (Bonus Action) makes some sense, but given the precedent of allowing movement inside of an Action and that the trigger for GWM is not the Action but an event, a GM could rule at their table to allow it.
Crawford's intent here is understandable, but it still doesn't make 100% logical sense given that you can already interrupt your action with movement and/or reactions.
At my table, I generally let my players shift and shuffle actions as long as they aren't actually limited by a clear mechanic. In this case, it makes more than good sense to allow the player this and I haven't seen any issues with it at my tables.
Best Answer
TL;DR
Details...
So, to clarify the scenario, we have three creatures. I'll give them names:
Bob charges, Jane. But Nelly has readied an action to move. As soon as Nelly sees Bob, she wants to run across his path directly in front of him. What happens?
First, a "charge" is not a discrete action. The Charger feat, PHB p. 165, says:
So Bob has taken the Dash action. Normally, Bob would attack Jane using a bonus action after finishing his move.
However, in this case, as soon as Nelly sees Bob, she interrupts Bob's move:
Page 193, PHB:
So, in this case, the "trigger" was "as soon as Nelly sees Bob". So, she moves, crossing his path directly in front of him, and provokes an attack of opportunity in the process.
Nelly, is the one moving at this point, so only Bob gets an attack of opportunity, not Nelly.
Even though it is Bob's turn, he can still take his reaction to make an opportunity attack, p. 190 of the Player's Handbook:
The charge feat allows Bob to make an attack as a bonus action, and possibly gain a bonus to that attack. It does not grant a bonus to any other actions, or attacks. So, Bob does not get a bonus to his opportunity attack.
From the Charger feat:
Next, after Bob makes the opportunity attack, Nelly completes her movement, and Bob's turn resumes.
Bob may continue his movement toward Jane, and use his bonus action to make an attack as granted by the Charger feat.