In my opinion, action economy is pretty powerful in 5e. So there's a pretty stark power difference between adding additional options they can do within their current economy, such as kobolds tumbling out of the way by spending their reaction, and adding in extra actions during the turn. That said the reaction and the bonus action are both tricky in that the creature may or may not have a use for it out of this, so it can effectively be an extra time to go.
I like the use of both in their place, but with the though that both a reaction if it was more likely they would have no reaction, or a legendary action, will take time and slow the cycle to get back to a player. The amount of time a player spends not interacting is, to me, an important metric. I will definitely spend it - foes and others going - but I want to make sure that it's spent in worthwhile ways.
Last time I did something like you were suggesting was in my Masks of the Imperium campaign, where the players are all agents of the Child-Empress and wearing semi-sentient artifact masks. Magic items that grow with them. They are currently on the rebelling against an usurper (-ish, but that's besides the point) and fought against another Mask Bearer who had his mask for 20+ years and had it a lot more awake.
So while he was wearing the mask it had a number of once per day reactions (like Hellish Rebuke and Counterspell) as well as it's own 1/turn reaction (so an additional reaction to what he had - so power-wise closer to a legendary action). But there was also a trigger where it levitated off his face and basically became a caster in it's own right (though without any Concentration spells). And when defeated went back on his face and continued with the reactions until all of the powers had been used up.
I like the technique, I try not to overuse it so it feels special - but listening to the idea of it being a norm does give me thought if I should try to incorporate it more.