But what is the border? Set the border to what it actually is, not a simplification of it. The state of Colorado is formally a 697 sided polygon, don't simplify it to a rectangle.
It depends on what purpose you are using the polygons. In an online map you need to simplify way down. Consider these Colorado maps at two different zoom levels:
https://maps.app.goo.gl/JH93ko96QcoLXuBJ9
https://maps.app.goo.gl/au53iTnsmNdFuEZV8
Even the one zoomed in on the state appears to use maybe 15-20 vertices max.
In the second one, if I squint real hard I can just barely make out one slight dogleg on the western border and one on the south. And that is partly because I knew to look for them in the zoomed-in map.
If we use, say, the Census TIGER/Line boundary definitions for the states, we are probably talking about hundreds of thousands of vertices, perhaps millions. You won't be using those in an online map without simplifying.
The Texas border with Mexico is formally down the centerline of the Rio Grande, even as the river moves (ignoring fiddly complications). Even if you could somehow take a perfect snapshot of it at a given time, you'd run into the coastline paradox when sampling it.
This is not what OP is describing. It is very common to simplify objects for decreasing boundary objects by orders of magnitude. GeoJSON is missing correlation when you do that. Simplifying country objects from a GeoJSON source could lead to a gap between the country borders. So you either have poor representation or a longer pipeline to convert objects to an amenable object set. It also breaks idempotency in some regards.