I can only speak about airline flying in general as that is what i do for the most part. But flying any european registered airplane with a JAA license is perfectly normal. And no, aircraft do not have to be based and maintained in their country of registration, however you might have to deal with the authorities in the country of registration in regard to maintenance and airworthiness.
EI-registered aircraft are very common all over europe and even outside the EU, for example in russia.