Because european options can only be exercised on expiry the value of the options react differently from american options, especially with regards to the intrinsic value component. As american options can be exercised at any time one can get access to the full intrinsic value when in the money - with european options I don't see how one can get access to the full underlying intrinsic value without having the ability to exercise at this precise moment... Option writers know this and there is much less hassle in managing european options than american options - could this be the reason we're not seeing any american options?
The bank is in a much more secure position with an American warrant. The maths behind the American instrument must be quite a bit nastier to manage too. Since "we" never exercise these things - perhaps the European model is truer. Why pay for a right you will never benfit from?
Personally - I have no joy with these hopelessly complex instruments regardless of American vs European... They always find a reason way to decay at breakneck speed and ruin my sleep. Haven't touched them in years.