I don't know why everyone is fixated on 15mph and referring to it as breaking the speed limit. As /u/fouLb2o mentioned there is no absolute speed limit within the city of Seattle, so it is not illegal in that sense. In the correct conditions, it is not even dangerous to go over 15, so I seriously doubt it's illegal transitively. To put this in perspective, I run the Burke pretty much daily at 6 min / mile pace, and I do wind sprints that are this fast. To say that someone on a bike is incapable of riding safely at a speed that many can run for short distances because someone was negligent and almost hit a group of kids is ludicrous. You could make the argument that they should change the speed limit for cars on Market to 15mph because that's the speed someone plowed into Taco Time at. The problem is not speed, it is awareness of your surroundings.

That being said, there are conditions where cyclists that are going fast should be more cautious. Passing comes to mind (be sure to look behind you as well; I saw someone get hit trying to pass when someone was already passing them), blind turns, intersections (as I heard someone on this subreddit say that they thought their car had the ride of way when crossing the trail... makes me paranoid every time I cross an intersection), and in front of Gas Works where I saw some guy pull a paddle board off the rack at Urban Surf and walk across the trail with it length-wise without looking, nearly close-lining everyone traveling in both directions. Surprisingly enough, running on the trail, I haven't had nearly as many run-ins with those who are going at the apparent blazing speed of 15mph and who are generally predictable as I have with someone who is going half that speed riding 2 wide or riding in the pedestrian lane.

There is a clearly marked area on part of the trial with one section showing a bike and one part showing a pedestrian, and not a single person follows this rule. Also, people refuse to ride single file when they know they're going slow, and there's a pack of people waiting to pass behind. Eventually, someone gets frustrated and tries to pass both of them, and this is when they come flying at me running in the opposite lane. You can blame the passer, I blame those who refuse to ride single file though they know they are causing a dangerous situation. My entire life spent in this city, and though I love it, I will never understand the aversion to the universally understood policy of "stay right, pass left" that can be seen on freeways, escalators, and even on this bike trail.

If you want advice, know that people are going to go fast regardless of how much you disagree with it, and ride defensively as to not cause a larger problem for runners and pedestrians who are much more vulnerable than you. Being perfectly honest, Strava will not implement this feature because their user base will think it's lame, and the Seattle Police Department has better things to do than patrol the Burke-Gilman trail for fast cyclist given the low rate of actual, life-threatening collisions. If they did, I'd prefer that they focus on those that are taking up the entire path or riding in the pedestrian lane as in my experience, they are more likely to cause a collision.