I say this as someone this applies to
If you are bad enough that you run out of vials and need to farm them
then you are bad enough that you need to stop trying a boss and go and farm vials for a while.
I know that sounds like a trueism. But like seriously. It's true.
You need to take a break from what ever you are doing and work on giving your brain space to stop and work through that shit in the background while you work on base mechanics again.
I know that's humiliating and boring, but this is a hard game. Those in this thread who did not ever have to farm are better than you. That, and they also do not use as many vials, because they play more aggressively, using enemies to get health back, and not using vials like estus flasks.
Bloodborne is not a game about playing exactly how you want to in an RPG. It is a game about frantic, aggressive, but skillful action. The game systems are designed to encourage you to learn how to play that way. If you are running out of blood vials, you are bad both at playing the game as a player, and at adapting to its style of combat and confrontation.
This is not a dismissive "git gud." It's coming from someone who farmed a lot of vials because I was bad. As I continued, I farmed less vials. It sucks, and it's humiliating, but you don't get better by protecting your pride. Get better at the game. If you want to stop running out of vials, stop using them so much. If that means you die more, then you are bad at the game. So get better, and stop using vials when you don't need to. Take risks. Learn when it's appropriate to hack back health. They are not estus flasks. They are consumables to top off after you've failed to regain your health. If you always got free vials, you would not have to be good at this. Limiting vials to a smaller amount would limit how levels could be designed, and it would make it harder for players who just are not as good. I got better at the game as time went on but was never able to get through some areas without using all my vials. This system allows the game to be adaptable to various skill levels, while also requiring all skill level players to take the time to improve.
The game is not poor because it doesn't allow you to play passively. It's not poor because it demands you get better at the game or stop for a short while because you are wasting your time bashing your head against a wall. The game does not want you to win just by random chance, which will eventually happen if you bash your head against a wall enough (this is also why typically lamps are not right next to bosses; it slows that down). The game wants you to get good at the game, because getting good at bloodborne is really REALLY fun. But it doesn't happen if you don't want to change.