When formally conducting the study to determine this, even those not having dog pets generally agreed. Wildlife disruption, thrash-strewing & the like, is mostly a people problem. Even in communities that had concern for wildlife with similar canine characteristics, none were caught or killed by dogs.
This was in regards to a prairie dog population. A dozen scientists spent over a quarter of a year looking into this. Yes, due to smell & other issues once the prairie dog caught a canine scent, they became more edgy. But in the final analysis, it was determined that a pooch was not a threat.
Whoever wants to make a case for ecosystem disruption while having domesticated dogs around, would most likely have to admit an overwhelming human presence already doing that. Over 90% for people vs less than 50% for canines.
There might not be an inherently researchable way to show the need for a dog to be off the leash. But ask a scientist that has grappled with the inquiry, & its educated guess would point one to a compelling reason.
Even if anecdotally, a dog that is happiest is shown to make a happier dog owner. Bettering emotions on humans tends to have a better effect on sound decisions that would likely lower the possibility of environmental disruption.
When dogs are on a leash, it’s as if they’re told there’s definite area to protect. That increases their aggressiveness towards anything that comes near the area pre-determined by the rope. When a dog is off the leash, it’s a more natural process of interaction with other canines & on areas considered as neutral.
Being on a leash also increases a dog’s frustration in other areas. If going on a walk, it either has to wait or try to keep pace with the owner. If allowed to not be tied, a dog’s anxiety level seems to come down in terms of getting its curiosity satisfied.