I wasn't literally suggesting that you store offsets. Or timestamps. There are way too many weird cases around doing that. But "America/Los_Angeles" is a reference to a file in tzfile(5) format, which contains, among other things, the UTC offset. And a function that produces the correct date and time in Los Angeles at any point in the past has to know (among other things) if that offset was ever anything different, and if it was, when it changed. And many other things.
There are date/time libraries that can't get all of this right, but you'll come a lot closer using them than you will rolling your own.
Don't store raw timestamps. Don't store offsets. Use date/time data types.