As a dog owner, Chad, I get your point and I very much accept the responsiblity to make sure my dogs' by-products don't undermine anyone else's enjoyment of public premises. But the problem you've raised applies to places besides athletic fields. For instance:
Several areas of Water Plant Park look like Dresden would have if a St. Bernard had been in charge of the firebombing;
For some unknown reason, there is a flower/sod bed right outside the back door to the VA Hospital that is just plain solid dog 'pooh'.
I'm sure there are many, many more examples of dogowners allowing their pets to use public greenspaces as personal comfort stations., much to the detriment and displeasure of the rest of us. And I agree with you Chad - that's pretty selfish behavior.
Truly responsible pet owners carry plastic bags with them to "pack it out" -- or at least take a shovel and a bag once a week or so to clean up the areas their dogs soil on a regular basis. But that's pretty uncommon behavior, which is why you end up with stinky stains on your jersey or smelly deposits on your shoes --- usually right before an important meeting at work.
I think one problem is the "no dogs allowed" rule in City parks. I'm a firm believer in leash laws in places where dogs and people will intermingle. Unfortunately, the current law is very good at preventing the City from providing "doggie dooley" stations (trash cans and plastic baggie dispensers that facilitate responsible poop-scooping by dog owners), but is very ineffective at preventing dogs from entering (and using) the parks. Yet another example where an overly strict regulation exacerbates the very problem it is trying to eliminate (npi).
I think we would all benefit from finding a reasonable compromise where dog owners are able to enjoy the company of their beloved pets as they play in the parks, while at the same time we are able to more strongly enforce rules to keep the parks 'pooh-free' zones and prohibit dogs from accessing athletic fields - which is the one and only place (imho) that dogs truly never belong.