The Commonwealth was really more Fascist and fundamentalist Puritan then democratic. Reason it had a Rump Parliament.
To elaborate, the "Parliament" that Cromwell dissolved was already the product of a military coup. After the second round of the ECW was over and King Charles was recaptured, many of the Army's leaders split with the Long Parliament over what to do with him: the prevailing opinion in the Army was that the King was incorrigible, and executing him and abolishing the monarchy was the only way to avoid endless civil war, but a majority in Parliament (including a number of outright Royalists who had sat in the
Oxford Parliament during the war) wanted to try once more to negotiate a settlement.
The debate ended with
Pride's Purge, where two Army regiments set up shop in from of the entrance of the House of Commons and turned away anyone they didn't consider reliable. In all, a bit more than half of the Long Parliament MPs got purged or walked out in protest. The remainder became known as the Rump Parliament.
Cromwell's dissolution of the Rump Parliament came five years later, after they'd gone back on an agreement to set a new constitution, dissolve, and hold new elections. Hence the best-remembered parts of Cromwell's speech: "You have sat too long for any good you have been doing lately" (13 years and counting since the last election, back before the first round of the Civil War) and "I say you are no Parliament" (asserting that the legitimate Parliament had ended with Pride's Purge). To his credit, Cromwell actually did (after a few false starts, most notably the
Barebones Parliament) hold new elections under rules that were arguably the fairest and most democratic of any British parliamentary elections until after the Reform Acts.