If I was a frog, I really would not like to be caught by a cat, even I was subsequently 'released'.
You might think that the cats and frogs are just playing, but I don't think that the frogs see it quite like that.
I have plenty of frogs, and there's a cat around. But there's no trouble. The cat really does prefer to spend its time patiently waiting to try to catch mice. Cats love to catch mice more than anything else.
You need some mice.
..Just off to catch a mouse that Ellie cat has brought in
Oh, you've already got those too, have you 


I would not have thought that being picked up by a human was more detrimental than being picked up by a cat.