Not sure if I fully understand what you write here.
Sure you can define rest intervals time based and when you stand in these intervals, the clock ticks further.
If you define your rest interval distance based, of course standing lengthens your time in the rest interval.
What
@James.K.Polk wrote:
"One concern is more practical - when you’re taking standing rest, auto pause fires (so you need to remember to turn that off, and as far as I know, you can’t do that mid-run. "
Assuming you have a time based rest interval and auto pause enabled (which is not the case in practice as Apple switches it off in interval workouts). You would stand in a time based rest interval and your watch would detect: "this guy is not moving, I pause the workout". You would end up with an infinite rest interval or at least as long as you desire to not move (which is ofter longer than what my interval workout wants from me ;-)).
If you are not clear how long the rest interval is, you could either manually pause the workout during the rest interval or define an "open" rest interval and progress manually to the next interval.
Hope that clears what I meant?