That's true about damage being more likely in Bloodborne, but I'd say you could adjust for that by changing the number of vials given by default. You can't increase max health or healing per vial because that would affect difficulty. Higher max health means you could take longer combo strings to the face without dying and more healing per vial cuts down the time you spend in a vulnerable state to heal in combat, but simply giving you more vials allows for longer runs without affecting the difficulty of individual encounters, so you can tune around that.

Personally, I would be fine with the game being even harder by letting you carry fewer than 20 vials, as long as they're free. I would be fine having no vials whatsoever! Like I said, the difficulty isn't my issue. Make the game more difficult, I don't mind, just stop interrupting the fun part to force me back to an area I've already mastered to farm items. I know I'm not technically "forced" to use them, of course not, but they're there. The game is balanced for them. Choosing not to use them just so I don't have to farm is choosing to put myself at a disadvantage and play an overtuned version of the game. The game would effectively be punishing me for having the audacity to value my time.

Luckily, this never came up during the first two bosses. I'm sure I dropped below 20 at points but I never ran out completely, thanks to Yharnam's villagers dropping more. However, I did run out while attempting the Blood-Starved Beast, and doing laps around Yharnam to collect blood echoes that weren't even going toward levels wasn't nearly as fun as observing the boss and testing new tactics. I could clear Yharnam without taking damage and I could clear the route to the boss without damage, but I was still learning how to deal with Blood-Starved Beast and burning through a lot of vials to do it. Eventually I ran dry and was forced to take a break even though I was making progress. I've thought about simply not using vials at all on bosses until I feel competent enough to beat them, but then I'm substituting time spent farming with time spent running back to the boss far more often because I can't extend my practice sessions by healing.

At the very least, some enemies in every area should drop vials and it should be possible to respawn them without a loading screen, just to make the farming a little less of a chore.