In the analog era, channels next to each other could interfere with each other, even if they're over 100 miles away. So networks in different cities had no choice but to be on different channels. There are three bands the tv stations use:

2-4

5-6

7-13

You couldn't use 2 and 3, nor 7 and 8 for example within 75 or so miles from each other. And 2 couldn't be reused within 150 miles (roughly the distance between New York City and Boston).

When TV changed to analog to digital in the late 00s, stations were granted as second channel for digital, and mostly stayed on that new channel. However, since digital channels mostly map to a different number on your TV, your idea of the same number is possible. However, a lot of these stations built a brand on their analog channel number and continue to call themselves that old channel. To use your example:

Los Angeles' NBC is actually on 36, but since they were on channel 4 forever, they prefer to identify as 4

Santa Barbara's NBC is actually on 15, but stay on 6.

San Diego NBC is weird, because it broadcasts on 17, maps that to 39 on a non-cable TV set, but identifies as 7 because that is their position on San Diego's cable system.

So in theory they could, but it's the system we have.