If the rule in DnD was that you got an opportunity attack on every character that moved past you in combat, and then BG3 only allowed you to get one opportunity attack, people would be screaming. They'd be saying how the BG3 system was broken and dumb for only allowing one opportunity attack.
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The problem--the "bad idea" if you will--is creating a system where every player is so precious that they get to decide which action the bard inspired them on that one time long ago when the bard inspired them. "Hmm. I rolled bad. I guess I'm gonna say that I'm now conveniently inspired from that bard who inspired me hours ago."
I am now questioning if this thread is an actual serious suggestion, or is in reality a thinly veiled attempt to snipe at another faction on the forums.
I quote your last line because if your primary argument revolves around the existence of some bad idea and trying to use that as justification to suggest something else, you'd better at least make sure that the bad idea that you're framing your entire argument around actually EXISTS to begin with. For one, you can't hold onto a Bardic Inspiration die for 'hours', a party member can only hold it for 10 minutes maximum. And it only lasts for that long because 1) it's a class feature exclusive to Bards and not some spell that multiple classes can share and 2) it also has out of combat applications.
Even then, I can't think of anything else that exists in all of DnD that lets you hold onto a resource to use as a reaction for such a lengthy period of time (let alone something else that lets you outright give a reaction to another party member), which is probably why you've latched onto that nonexistent bardic inspiration argument. Maybe the closest thing would be Guidance, of which the Guidance bonus can be maintained for up to a minute as the caster is able to hold onto concentration.
And quite frankly, I'm pretty sure Larian has already thought about unlimited reactions or something similar, and decided against it for reasons close to what I've already brought up earlier in the thread. Even if actual DnD 5E had unlimited attacks of opportunity, it's assumed that the rest of the system would have been meticulously balanced around its existence. The changes Larian did while omitting reactions were basically too many haphazardly thought out adjustments at once for them to have worked out in the long term, hence the majority of them being rolled back over the past year. And as another example that most people here probably aren't aware of, Solasta actually did have one major homebrew rule at the start of their EA (of which dim light used to impose disadvantage), but enough people universally complained about that to get it struck down. Not because of official rules, but because dim light disadvantage coupled with some Solasta enemies having the ability to walk on walls and fly made fighting such enemies
extremely annoying.
Even so, judging from my limited experience of DnD 3E by playing the Pathfinder cRPGs, effectively unlimited AoO -was- possible there if you built yourself for it, but there were also a lot more conditions to trigger them AND avoid them too. (In those games, you took opportunity attacks for each spell you cast or arrow you fired with an enemy next to you, so long as that enemy had enough available opportunity attacks to punish you for it. It appears that got replaced with disadvantage in 5E instead. You also used to take an opportunity attack when standing up from being prone, but no such penalty exists in 5E.)
And if you're going to rail against purists on this forum again... Consider that we've already long since established that there aren't really any purists on this forum. Yet again, there's a huge gulf of difference between 'wanting certain things to be closer to the rules because they're better balanced than the new stuff' and 'wanting things to be closer to the rules because they're the rules'. For example, no one is complaining about Sorcerers getting spells based on their bloodline, because that is a legitimately good change that has an effect on character customization. I personally want to see Paladins have the ability to smite with ranged weapons too, and I doubt there'd be very many people that would disagree. For the topic of reactions, people feel THIS strongly about them because some classes, spells, and abilities are extremely reliant on them, and omission of those throws off the balance by quite a lot and pushes the game towards heavy offense tactics, not leaving much room for defensive considerations.