The two most distinguishing features of vampires are the sunlight allergy and the fact they feed on human blood. So if you're playing Vampire instead of Mage, Werewolf, Hunter or D&D, it's expected that you're somewhat interested in the idea of playing an undead monster that preys on people at night.
From a game design perspective you then want the player to care as much about preying on humans as the vampire does, the player should be thinking about how to get their next fix of blood. The way most games choose to do this is by making all the vampires special powers fueled by blood, requiring the player to regularly find a source to renew themselves. In VTR/VTM the vampire also loses blood daily requiring them to find blood sources even if they're not actively using their powers.
Since being a predator is such a big thing about vampire, you ideally want feeding to be something that's done on screen, in video games you'll usually have a feeding attack you're expected to use regularly. However in TTRPG's or MU* it's not practical to have every feeding event on-screen however since it's still a big thematic point, you'll want some mechanic that makes the player pay attention to when/where they feed. In TT that usually means making a roll with some sort of modifiers and if you fail, then your feeding went awry in some fashion. In MU* however you can take the opportunity to play up another part that's a big part of being a predator, territoriality.
By making blood limited on a grid-square basis (Abstractly representing the difficulty of getting away with several feedings in the same area in a short amount of time) you make the players care very much about who feeds where and when. It's in their interest to control some part of the grid and determine who feeds their in order to guarantee their own supply of blood as well as being able to offer blood supply to others in return for favours.
Talking about the chances of getting away with feedings based on population numbers is missing the point. Handwaving feeding in Vampire is like handwaving breaking&entering in Shadowrun or exploring the dungeon in D&D. Regardless of your chances to get away with it, it's something you're expected to care about and you want complications to happen somewhat regularly so you have the opportunity to use your fancy vampire powers to make them go away.