The use of 'got' in a clause describing possession of something, such as 'I have got a pen', is superfluous. 'I have a pen' is just fine and indicates a brevity and clarity of thought that eludes many people. It may also indicate the influence of other languages. In French 'I have' is normal. I'm not sure how you would say 'I have got' in French. In fact in French you don't need the addition of 'got' to convey meaning or emphasis. French does seem to have a brevity that English has lost over the years. Around 60% of the English vocabulary originates from French. The Norman invasion of 1066 established French as the language of nobility and government, Latin was the language of the Church and Anglo-Saxon was for the commoners. 
I am an Englishman who has spent many years learning English so I feel I am entitled to criticise the language and especially those who use it badly. Perhaps it's the Germanic influence on English that has caused the gradual creep of 'got'. American English has certainly been a big influence  on the language. A good example of how American English has been a positive influence eludes me at the moment but I do know they exist. The German language had a big influence on American English and in my opinion this comes through in expressions such as 'gotten'. It's a natural progression on the word got but it definitely grates on the British ear. 
The next time I watch a British movie of the 1930s or 1940s I will note the use of the word 'got', although the scripted dialogue may not be a good indicator of common usage. 
Grammar is the set of rules used to govern the use of spoken and written words. As with all rules, some are so rarely enforced that they wither on the vine of principles until extinct.