This is bothering me, still.
Many limited company directors may not be 'the worst off in society' but they are small business people basically working for themselves in tiny companies, and they have incorporated mainly because they have been required to by their clients or quite reasonably seek to avoid unlimited personal liability.
The choice to pay themselves partly or mostly through dividends is not some 'fat cat' scheme dreamed up by lawyers in the Cayman Islands, but a legitimate option made available to them by normal UK legislation and HMRC rules.
The tax advantage is certainly NOT 'pay 7.5%' vs 'pay 40%', but it is complicated and I don't know the details. I seem to recall my accountant saying it was 'pay 21%' or 'pay 25%'.
Any such tax advantage is a tiny privilege for going without sick pay or holiday pay, and bearing loads of personal income risk. If the proposal I have been working on all month is not accepted, then I make no money. Big company employees in PAYE tend to get paid whether they work or not.
And I am not taking advantage in other ways as some do. I have not declared Verbier as a suitable place to go on a February business research trip (unlike 80% of those on a recent 'boys' ski trip), I have not made my wife redundant to collect £30,000 tax free (as a friend of mine did, twice), and my children's mobile phones are not company phones.
It seems to me ridiculous if a, say, a painter & decorator with billings of £26,000 per year, which he has been taking out of his company through PAYE can get £1,700 a month, but if he has been taking it out through £10,000 of salary and £16,000 of dividend he gets £600. (I suppose you could think of that as a 65% tax rate on the payouts - doe that seem fair?) And if he and his wife work together in the business and were billing £52,000 a year between them, then they get nothing.