Plenty of people criticise the IMF and other institutions for all kinds of reasons, you don't have to do much research to find comments about it.
I mean if you own a business worth £15m then you would pay £300K per year, what happens if you don't make a profit or don't have £300K in liquid money to pay it. Do they sell part of the business? Insurance companies don't value companies all the time, they provide liability cover etc based on some company information but they don't value all of them (I'm sure they do value some). Are the government going to pay for every company to be valued and then administer the whole system? What about all other assets, do the government pay for them all to be valued, how often are they revalued and who manages all of that?
Why listen to me - you can read it for yourself here including this quote from your friends at the IMF?
Claims of £24bn from a UK wealth tax ignore delays, capital flight (£200–£500bn) risks to growth and employment. Data, country evidence & better reforms.
taxpolicy.org.uk
Your examples mostly show that a wealth tax would need sensible rules, not that it is unworkable. Every tax has edge cases: income tax, capital gains tax, inheritance tax and corporation tax all have valuation, liquidity and enforcement issues. The existence of complexity is not the same as the policy being impossible.
If someone owns a £15m business, the obvious answer is not ‘the business must be sold.’ A well-designed wealth tax could allow deferral, installments, or special treatment for genuine trading businesses, especially where the owner is asset-rich but cash-poor. That is a design choice, not a fatal flaw.
The valuation point is overstated too. Businesses, property and other assets are valued all the time for lending, insurance, probate, accounts, transactions and tax. The state would not need a perfect valuation of every asset every day; it would need a workable system, just like every other tax does.
As for who administers it, the answer is: the tax authority, as it does with other taxes. It would use thresholds, declarations, audits, reporting rules and anti-avoidance measures. You don’t reject a tax because it needs administration — administration is part of how taxes work.
And on the IMF quote, that does not mean ‘wealth tax can never work.’ It means the IMF generally prefers better capital gains and inheritance tax design over a broad wealth tax. That is an argument about what they think is the better policy mix, not proof that a wealth tax is impossible.
So the real issue is not whether a wealth tax can be perfectly neat — it can’t. The real issue is whether the benefits of taxing extreme wealth outweigh the practical costs. Saying ‘it’s complicated’ is not the same as proving ‘it can’t be done.’