A big reason why the Roundheads wanted to make Cromwell king was to limit his power. His status as Lord Protector was not King, and therefore had none of the constraints on power that the kingdom had evolved over the centuries.
He wasn't widely popular outside the parliamentarians, who were the ones in power. The "godly", who made up the majority of the Roundheads were reviled by a substantial portion of the British. Cromwell held the Commonwealth together, that's for sure, but the cohesion amongst the Roundheads dried up once he died.
Source: The English and their History by Robert Tombs
He wasn't widely popular outside the parliamentarians, who were the ones in power. The "godly", who made up the majority of the Roundheads were reviled by a substantial portion of the British. Cromwell held the Commonwealth together, that's for sure, but the cohesion amongst the Roundheads dried up once he died.
Source: The English and their History by Robert Tombs