Newbie VOR question

Larry Dighera wrote:

You'd be surprised at how little the distance increases on a VOR route
compared to a direct route.


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You're probably right about the distance. But doesn't everbody flying
TO/FROM VOR stations cause air traffic problems like near misses
(collisions)? Or being aware of this do you just watch the skies very
carefully near VOR stations? Or are there altitude guidelines for each
radial?