The idea that the self employed should pay less tax because they don’t have steady income, or that they don’t get paid holidays etc etc annoys me.
That isn’t the taxman’s problem - the individual should be getting paid more to cover that (and contractors in the finance industry certainly do!)
Trouble is that the customer (you and me) doesn't want to pay the self employed person more. In fact, many actively go out of their way to find, say, tradesmen who'll work for cash to avoid VAT, or buy duty free booze and fags from a bloke with a van.
You're also missing the point that it's not "tax" where the big difference arises - it's NIC. Self employed pay a lower rate of NIC because they get poorer state benefit entitlements.
As for the like of finance contractors, when you factor in the loss of employer benefits (gym, health insurance, life insurance, pensions, season ticket loans, holidays, duvet days, training, redundancy, profit related pay, bonuses, enhanced sick and maternity pay/leave, etc etc), there's not actually that much difference - these people are mostly working for "big" firms, often multinationals, etc., so the "benefit package" of the permanent employees is often pretty spectacular.
I've had IT contractor clients who've moved from contractor to permie rolls in such places (Hiscox insurance, Deutsche Bank, etc) - and when you compare the "total" package under both ways of working, they're pretty similar in terms of cost/benefit. I had one female contractor client who "went permie" and then went onto maternity leave a couple of years later - she was tens of thousands of pounds better off by being an employee than she would have been if she'd remained as a PSC contractor due to the maternity pay/maternity leave, etc. Another client was a bloke in his 50s who likewise went permie, took a pay cut obviously, but then was diagnosed with cancer - the employer fully supported him during 2 years of treatment with enhanced sick pay, part time working, time off for treatment, etc - if he'd been a contractor he'd only have been paid for the hours he worked which again would have been tens of thousands of pounds less.
It's easy (and naive) to superficially compare an employee's hourly rate against a self employed hourly rate, but you need to bear in mind all the other factors. People need to appreciate that when you're self employed you don't get paid when you don't work, you have to pay your own pension, life insurance, "benefits", etc., you don't get redundancy, you often risk your personal assets, and sick/maternity pay/benefits are but a fraction of what a good employer would provide and state sick/mat pay isn't as good for self employed either.