Irish banks are nothing like US banks and they've become even stricter since our horrendous recession. Not only do we only have 1 credit card the limit is very small. I've been working all my life, no debt and that's the best limit I can get. My son cannot get a card at all and he's 25 with no debt and a decent entry level job. My husband is a contract worker currently on a 2 year contract so he has no access to credit of any kind without a permanent contract.
There's still a large portion of our population (and the UK) who have no credit card at all so it definitely makes US travel a headache. Although Florida experiences a lot of UK tourism so several companies down there accept debit cards and cash deposits.