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More arcane.
Seriously so.
I spent a while, a few years ago, going through two different legal areas from both a UK and an EU perspective.
First was libel, defamation and liability as it relates to online forums and user generated content. Second was tax, for sales and purchases by small companies within the UK and Europe, the reporting of, accounting for, etc.
To put it mildly, British law is arcane, not in one place, seemingly almost purposefully vague (beyond the vagueness one expects in law in the first place to allow for reasonable judgements and some fluidity).
European law in comparison was unbelievably simple to read, and apply.
One of the big reasons I voted remain was the economy, or rather... a belief that tax avoidance/evasion by multi-nationals was harmful to the economy of countries, and that we needed to take steps to simplify the tax codes, enforce more evenly, etc.
The EU is pretty clear about wanting to tackle this, whereas the UK is pretty clear about not wanting to tackle this (and supporting nice overseas locations to encourage it, and a tax code that will always leave big loopholes because no-one can ever know the whole of it).
If we're talking about things that Britain is a master of then bureaucracy, loopholes, doing our best to make sure that the rich don't go hungry all rank quite highly.
Brexit remains a nightmare for the City of London. And for the wider UK. What is it? 10% GDP or something? Fun.
I think your point about shedding unnecessary bureaucracy is a legitimate one. There is always a tricky balance between having checks and balances to protect society and not tying every element of life in knots.
That said, why does Brexit actually shed layers of bureaucracy? We will still need to comply to most if not all the regulations. In many cases have we not just in-sourced a whole load of admin that was previously being spread across all member countries? - which sounds decidedly ineffecient.