It is worth noting that Cromwell did take a number of months after The Humble Petition and Advice was presented to decide whether or not to accept the crown. It can be argued that this is evidence enough that he wanted the crown for himself, after all, he was King in all but name at this point. The fact of the matter is, that Cromwell's power base largely came from the New Model Army and its officers. The same officers who had during the First Civil war fought against the King for civil liberties and during the Second to depose him. Naturally, they would not be thrilled for their leader to become that which they had fought against, so if Cromwell had taken up Crown, he would have lost the support of his primary powerbase.

At the end of the day, regardless of whether or not Cromwell genuinely felt that he should become monarch or that he shouldn't, he could not feasibly do it given his reliance on the Army.