​@StriveTerry my 2c… it may be irrelevant for you but it's very relevant for other runners. E.g. when training for a specific pace - you might have to stop e.g. at road crossings, but otherwise need to maintain a stable pace. 

When running a race, the elapsed time precedence makes sense. In a training, I sincerely don't care about elapsed time/pace, what's relevant for me is the moving time/pace. 

So, if you ask in what world it matters… in this one. ‍♀️
 

If you think it helps, they should make it an option, not the default with no option otherwise. 
You wouldn’t be able to do that pace without that rest, so it’s inaccurate in your example, anyway. And the race isn’t stopping the clock when you stop to tie your shoes. 
And even ignoring those factors and assuming most people wanted to do it that way (which hasn’t been the case with anyone I’ve talked to) that’s a setting you can do yourself in your watch. No reason for Strava to make everyone do it that way. 

“You wouldn't be able to do that pace without that rest” - duuude… what makes you think that?

Seriously: training is NOT about running “as fast as you can” every single time. Actually the opposite. You're supposed to do about 80% of your volume slow and only the rest is speedwork. And even that is not supposed to be “as fast as you can”, meaning that a rest would make the training faster or what. 
If I do, say, a marathon pace training 25k, then I want to maintain my M pace. Of course I can keep it “without that rest”, see it's a marathon pace, meaning it's supposed to be maintained for those 42 kilometres (and a bit). For a shorter distance, like 25k, of course I would be able to run yet faster - but it's a nonsense to do that, if I’m training for a specific pace. 

“The race isn’t stopping the clock:” of course it's not. And that's why, on a race run (which you can mark as such), Strava shows elapsed time, NOT moving time. Have you even tried that?

Seriously - you're attacking regular training principles here, calling them irrelevant, but it's all coming from your lack of knowledge, sorry.

I think both elapsed time and moving time are useful metrics. Elapsed time is more relevant for trail running, especially when doing multi-hour efforts. But knowing how much time you moved vs. elapsed time is very good signal too. However I’ve observed many times that moving time may be too “optimistic” on a steep terrain because Strava relies on horizontal speed when detecting movement, which can fall below the non-moving threshold on a very steep or technical terrain. Strava’s algorithm has improved over years, but it can still be inaccurate.

Furthermore, Strava has this magic trick that if you accidently press a pause button on your watch even for 1 second, that completely disables the moving time algorithm and uses the elapsed time instead. Often enough that is unintended.

I think it would be better to just display both metrics or let users choose which time they prefer.

So perhaps this idea could be a good solution for everyone: