Sure, but how often does one look at one's payslip? The money gets deposited in your account. I don't know about the UK, but the amount that gets deposited tends to vary because of small issues, so a different number on my bank statement doesn't trigger alarm bells.
It would be very easy to change my taxes without my knowledge as a result, if the only feedback we had on taxes was what was deducted from our payroll. In the US, there are deductions taken from the paycheck directly, including anticipated federal income tax (called "withholding" here) but also many other miscellaneous taxes.
The withholding, in particular, represent an advance payment on your annual income tax, which you still have to calculate and file. If you withheld more than you owe, then you get a refund, if less than you owe taxes. But regardless you have to compute how much you owe and how much you paid on an annual basis so that you can see it all at once.
Once again, I do not think this method works, but the theory behind it is that this will make it hard to quietly raise taxes, and hard even to maintain current levels of taxation, because it will be a painful process that will make it clear what the current situation is.