Mine have all got the temper etc for it but as they aren't neutered they aren't allowed to do it
Orion in particular was
*born* to be a PAT cat as he will meet someone for the first time and be all over them like a rash cuddling them and purring (he makes Bilbo look like he was anti-social!!).
One thing that rules some cats out as well is that they need to be happy on a harness and lead for doing it which a lot of cats aren't.
Mine however do it in an unofficial capacity for Findlay
He's currently having a hypersensitive day and is getting highly stressed by light, sound, textures etc but he currently has 2 x 4 month old kittens in his cot with him who are purring at him and happily letting him hold their tails and fur which is making him smile.