If there is any point in the national insurance fund it is to demonstrate that benefits are like a universal insurance system, paid for out of our money and due to us as predictably as an insurance payment or a private pension, and with the same kind of customers' rights and the same need for efficiency.
This is also a reason to end the idea of an "employer's contribution" in the headings which is a paternalistic fiction. Employers who calculate whether they can afford staff just have to work from the total figure rather than the advertised one. The transparency of the system would be increased if all the money put into it appeared on our payslips – perhaps from a date in a couple of years' time so we have time to prepare.
The second reason for merging the employer' and employees is to save the cost of payroll services. I've had a quick look at the table linked above and couldn't repeat it back to you or pay staff without help or hard work. This administrative cost is a tax on jobs that doesn't even bring-in any money.