Why did you shut it down? You say that it would affect the game significantly. How so?
Because it would invalidate entire encounters in droves, and led to an extremely asinine attempt at tactics repeating itself ad nauseum. Observe:
A bag of holding has a mouth that is 2 feet in diameter, and the bag itself is 4 feet long. The bag weights 15 lbs regardless of what is stored inside it, and it's inside is an extradimensional space that holds about 500 cubic feet of things. Removing an item from the bag takes an item interaction, and you can use an action to just dump everything out of the bag that is inside it. If you only go by measurements, you can in fact fit three to four average sized humans into the bag with their heads sticking out. They would be uncomfortable, and they would take time to get into the bag, but they would fit.
A flying character has a flight speed equal to their movement speed. The character in question was a Winged kobold monk a t 11th level with 16 strength (really good stat rolls). Since the bag is always 15 lbs, the flying character now has the ability to carry the entire party at 60 feet per round, or 120 if she dashed.
Additionally, there are no rules limiting flying beyond standard travel rules. A simple calculation reveals that traveling at a normal pace covers a distance of approximately base move speed x 8 = miles traveled. Base move speed of 3 results in 24 miles per day. A base move speed of 6 = 48 miles per day. A fast pace increases that speed by a factor of 1/3, so 3 becomes 4, and 6 becomes 8. 8x8 = 64 miles in 8 hours. This would allow my players to move over extremely large distances in a relatively short period of time with absolutely no penalties. Even using the teleport spell robs a player of a 7th level spell slot OR requires extremely rare and powerful items, often consumables, such as a scroll of teleport.
The tactic in question goes as such: Everyone rolls initiative. The Kobold moves in combat and flies 60 feet right toward the enemy. The Kobold uses an action to dump the bag of holding's contents out (containing the paladin, rogue, and barbarian). The Paladin, Rogue and Barbarian are now right in the face of the backline because the Kobold can simply fly over any guards or significant barriers. It is effectively a deep strike maneuver. Now I had to come up with a valid reason why EVERYONE with a bag of holding didn't attempt this same maneuver, or why the rogue in question didn't simply tuck his head inside the bag since it holds 15 minutes or so of air and infiltrate dangerous locations.
I also would have had to come up with rules for how to escape a bag of holding from inside when there is no real space to move, and whether or not being dumped out of a bag of holding would result in one falling prone, and how many other things in the bag took of space to calculate volume compared to the mass of the players.
And why would you think the obvious choice would be to shut this idea down? I know there are rules about how much fits inside, and I imagine a whole party of people may exceed that... but probably one or two people could fit.
In older editions, certainly there were rules that explicitly stated why this could not happen. But no, get out a tape measure and measure two feet in diameter. When you remember that it's an extra dimensional space, you just need each character to get in one at a time and they can, in fact, fit. You either then engage in large amounts of geometry to calculate volume, mass, space, etc, or you just assume that the bag of holding runs on the same type of physics as a clown car in a cartoon show, and all of the implications that this implies.
Imagine the Siege of Troy, if you will, with the Trojan Horse. Different historical texts lists the number of solders it held as anywhere from 30 to 50 men, so the Trojan Horse was quite massive. Now imagine that due to magical shenanigcans, the Trojan Horse is only the size of a poorly rolled up sleeping bag, but still carries inside it 50 Trojan Warriors fully armed and ready to go. Now imagine that those 50 fully armed Trojan Warriors can exit the bag effectively at their whim, without having to be in a line, or go one or two at a time, or get out first then reach back in to grab their spear and shield; no they just all spontaneously BAMF into existence in the space around the Trojan Bag. And since the bag is so small and weighs so little, really you don't even need to pretend that the rest of the Greek army is sailing away, you just sit on the beach and in the middle of the night, put 150 of your soldiers into 3 bags and sneak up to the gate and toss them over the gate. Soon as the bags land, you've successfully invaded the inner keep of your enemy.
BUT WAIT, I hear you say: There's two more inner keeps! Don't worry your pretty little head. Because there aren't rules that stop you from
one of the Trojan Warriors inside the bag of holding with 50 Trojan Warriors having another bag of his own with another 50 Trojan Warriors inside of it, and one of them has another bag with another 50 Trojan Warriors.
And now you see why I had to deny this.