The notion of a "line" is an abstraction we impose. Currently our memory works as follows: you provide an address to the memory module that you want to read, and it returns the value at that address; or if you want to update memory, you provide an address and the new value, and it overwrites the value at that address with the new value.
Why do we build memory that way? Well, the current way is simple and works, and can be implemented efficiently in circuits. If you wanted to consider some other alternative, you'd have to think about what are the benefits and what are the costs. I'm not clear on exactly how your counter-proposal would work, but I expect it would add complexity (which ultimately might add to the cost of implement the memory subsystem, and also might make the system harder to understand for programmers) without a benefit that would make it worthwhile. If you wanted to dive into this in more detail, you'd probably start by learning how RAM works at the circuit level. Our current RAM is highly optimized to minimize the number of gates needed, i.e., to minimize cost.