Of course the great irony is that he then arbitrarily dismissed Parliament himself (though the record doesn't suggest this was his actual goal) and was so unpopular in power that the restoration of the previous king's son to the throne on his death was inevitable. He certainly wasn't the poster boy for the development of British democracy, but he influenced its development massively - positively and negatively.
There is a decent chance that Parliament would have overthrown and executed Charles I without his military skill or enthusiasm for regicide (just like similar massacres in Ireland would likely have taken place without his -disputed- involvement and apologia) as he wasn't even a significant figure at the beginning of the conflict, but those whose name and public statements becomes most known always get the credit and the blame.