I would say because 'gotten' is a past participle and your sentence is in the present 'I have got' :- right now, I've got time.
Gotten is used in US English, but not in UK English. I understand that in the US one doesn't usually use 'have got', eg. 'I have got a brother', but rather would say 'I have a brother'. Using 'have got' is more common in the UK.