With sports where competitors aren't really facing against each other like running, why don't people just record personal bests and compare? I get that there's the competitiveness and mental aspect of sports but with running and vaulting and such, why not just record personal bests and sorta make that the official ranking? (I'm not a sports fan, just curious)

For two main reasons,

1. how do you standardise the event being taken so that it can actually be compared (distance? elevation and changes? wind direction and speed? surface type and condition?)

2. how do you certify the PB time itself is accurate and credible?

And for a host of other benefits, those are both taken care of by getting the measurements at the same place at the same time.

Also, a PB is only an indicator of what you have achieved perhaps once or twice ever, and may have been years or decades ago. That's the point of (national, world, Olympic) records - the purpose of competition is to find out who is the best right now this very hour or day.