Religious freedom was far greater under the Commonwealth than under the monarchy, thanks to the disestablishment of the state church and Cromwell's personal belief in toleration. The Church of England, ruled by the King and his hand-picked bishops, was far closer to a theocracy; and unlike the Puritans they were committed to enforcing religious uniformity. Also, during the Commonwealth the House of Lords was abolished and the suffrage greatly expanded, so that the Parliament elected in 1654 was the most truly representative parliament Britain had ever had until the mid-19th century.
All reasons that the Commonwealth appealed to me at a cursory glance, but you left out the autocracy of the Protectorate period (while there were theoretical limitations on Cromwell's power, in practice he was a monarch with an advisory council and a parliament) and the morality laws. The Council of State was dominated by the Army and the Barebone's Parliament was drawn mainly from the richest 5% of the population. It was a Bonapartist situation. Maybe the Commonwealth could have become something better than the Kingdom had it lasted, and you're right that some good ideas went into it, but it didn't. For all of its history, Cromwell had outsized influence. I don't consider that an improvement. That's just swapping out the old feudal elite for Cromwell and friends and slapping the republican label on it.
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