cats do benefit from outdoor time:
Fun things to smell, things to see, exercise, so on
however,
cats are invasive predators
1 ) Directly killing birds
(Lepczyk et al. (2004) Landowners and cat predation across rural-to-urban landscapes ; Pavisse et al. (2019) Domestic cat predation on garden birds)
...
2 ) Indirect killing birds that are rendered vulnerable by other circumstances
(Rebolo-Ifrán et al. (2021), Cat and dog predation on birds: The importance of indirect predation after bird-window collisions , which also mentions dogs but dogs-on-leash are more normalized than cats-on-leash)
...
3 ) Sub-lethal Fear Effects as birds alter their behavior as they're afraid of cats
(Beckerman et al. (2007) Urban bird declines and the fear of cats)
cats can threaten endangered species outside of being predators
1 ) Domestic cats mate w/ endangered wildcats like the Scottish Wildcats, with hybridization so common that some conservationists consider the wildcat genetically extinct ...
"in the five [areas] surveyed in 2017/18, the total ratio of wildcats to un-neutered hybrids was almost 1:6. Hybrids have become so common that wild-living cats in Scotland show a hybrid swarm structure, hence a continuum from domestic cats to pure wildcats." (Breitenmoser et al. (2019) Conservation of the wildcat (Felis silvestris) in Scotland)
overview might be worthwhile if you're interested:
Loss et al. (2022) Review and synthesis of the global literature on domestic cat impacts on wildlife
"Most studies (56; 88.9%) evaluating cat impacts on wildlife populations (e.g. abundance, extinction probability) or communities (e.g. species richness, total abundance of broad groups such as all birds) documented negative effects on at least one response variable. Only seven (11.1%) studies found no significant (i.e. neutral) effects of cats on any response variable. Although no studies showed only positive effects, eight studies showing negative effects also found significant positive associations between cats and one or more response variable. One of these studies found a positive association with species richness of non-native birds, and six found positive associations on some oceanic islands where cats are top or middle-level predators that, in some cases, suppress negative impacts on wildlife by depredating invasive predators such as rats."
(note on the rats issue, this is known, they hunt both birds & rats, and cat-culling allows rats to surge and hunt more birds. Suppressing both is needed.)
AND
unmonitored / loosed free-roaming is unsafe for cats
cars. poisons. bigger predators. bad weather.
in my mother's case alone, in just my lifetime, five different instances of her cats killed or injured because they're allowed to dick around outside without someone checking what they're doing. five. only two cats I can remember are unscathed (one passing of old age when I was young so not much lifetime overlap, the other a real homebody).
basically,
if you love animals, don't let your cat run around all over. They're smart and nimble enough to get into Situations, but afaik their intelligence is similar to a toddler & their understanding of cause-and-effect is underdeveloped.
don't let your toddler-who-can-climb-walls run around outside at night, they don't know what cars are.