Is there a chance you're misreading sports park to be a more general park, versus what the OP is referring to such as a facility with 10 soccer fields or baseball diamonds?
Check out a satellite photo of central park! So many baseball fields. I'm in a small city (denver) and have tons of 'sports' specific fields within walking distance.
No. That’s just not how the concept of density works.
For example, A 5 mile radius city has x baseball diamonds in it. That’s x per every 78.5 square miles.
Let’s say the suburbs of that city are a ring of width 25 miles with y baseball diamonds in it. That makes the baseball diamond density of the suburbs y per every 1885 square miles.
I’ll spare you the math x=24y give or take.
Then I encourage you to go to google maps and look at America’s most notoriously crowded cities like nyc, sf, Boston, Chicago. There are dozens if not hundreds of baseball fields in city limits. Central park’s 26 fields alone would need to be offset by 624 in the suburbs to achieve equal density.
The “problem” is that most of those diamonds are difficult to drive to and park at, which is why OP considers them non-existent.