Cromwell is probably the most complicated character in British History, in my opinion, and easy answers aren't often applicable in his case. But I'll try and give a couple of reasons why I don't think he would make this move:
1. Practicalities - Why does he need to? He already has power over the country through the Major General system and is trying to consolidate a working relationship with Parliament. Why risk everything with such an inflammatory move that is, essentially, little more than window dressing?
2. The Army - A number of the Army commanders that Cromwell relied upon were...not keen. Not keen at all on the idea. According to Thurloe, Cromwell's Secretary of State:
Protectoral Privy Councillors General John Lambert (one of the principal opponents of the offer of the crown to Cromwell) and Colonel William Sydenham...[spoke]...‘very earnestly against it and very few of the soldiers pleased with it so far as could be perceived’.
I can't find the reference but when one Colonel heard of the Humble Petition that offered Cromwell the Crown OTL he essentially swore and said something along the lines of "over my dead body".
3. Public Sentiment - the nation had just been through a Civil War and was starting to calm down. But it was still politically, socially, and culturally volatile. It's only been five years since fighting in the Third Civil War ceased and tensions are high.
4. Cromwell's own beliefs - hardest to get to and most controversial of the reasons, but a problem indeed. Would Cromwell, who was conflicted deeply over the idea of being King, really go further and go for something as extreme as "Emperor"?
Cromwell and Napoleon's cases are very, very, different in terms of circumstance, context, and character.