The only reason tracks are 400 meters is so that a football or soccer field can fit inside. A really dumb reason that makes running events an after thought.
Speed skating tracks are 400 meter ovals, and events are 500m, 1000m, 3000m, 5000m, and 10,000m. Running just needs to add 100m, 200m, and 110m hurdles (same as is done now). See the image link to the speed skating starting lines. No problem.
The biggest problem with 1600m events is that American kids think that is a mile. A kid will says, after running on a 400m track, "In training I ran 20 laps, 5 miles." No, to say you run 5 miles you needed continue around the first curve and more than half way down the back straightaway.