I’m sure it would be tough to have Strava automatically remove rest times from overall pace (one man’s rest might be another man’s workout), but Strava should allow me to identify rest “segments” in my uploaded workout. Strava can then ignore them when calculating pace and give me a true average pace. Example, I run 8x800m with 1 min standing rest - Strava will mark my pace as slower because of the 8 minutes of standing rest. When we mark the type of run as “workout” I would think Strava could account for rests.
Even better would be for Strava to put my splits on the main workout overview instead of having to drill into the workout.
What I usually do is creating a custom workout in the watch, so that those intervals are recorded as “work” and the jog/walk in between as “recovery”; and each is automatically marked as a lap, so that when reviewing the workout later on, I can easily see the “work” pace, and ignore the “recovery”. (This is with Apple Watch; not sure what device you're using, but I assume it will be similar with other devices.)