From DMG p.139, "Most potions consist of one ounce of liquid." Just to clarify the amount of liquid we are dealing with here.
From PHB p.197, "If damage reduces you to 0 hit points and does not kill you, you fall unconscious (see Appendix A). This unconsciousness ends if you regain any hit points."
The most obvious answer to this would just be "Rule of Fun" - it's going to be really boring for the other characters if they have no other method of healing, and have to just sit around waiting for the unconscious person to regain a hit point after 1d4 hours. That's not even considering other possible trouble, if they happen to be somewhere it isn't safe to just sit around for several hours.
If that doesn't work, consider ways around it. While drinking a potion is considered the standard application method, it doesn't have to be the only way. Dribble the potion over the other character's wounds, or maybe even just splash it at them. It is rules-legal to administer a potion to someone who is engaged in the middle of melee, and I can't see whatever they are fighting taking a step back to let someone heal their opponent.
Additionally, there's always the "it's magic" excuse. Perhaps part of the magic causes the person to swallow it automatically, or maybe it works like mouthwash - swish it around in your mouth so the magic soaks in, then spit out the now-useless liquid.
It's considered rules-legal by the designers. It's reasonable based on extrapolation from other instances when applying potions are legal. It makes the game more fun, and proceed more smoothly.
If none of these reasons satisfies you, then don't allow it.