Employee NICs and employer NICs are effectively the same thing, they just have different names. Your employer has a bucket of money to pay employees with. Some of this money is given to the government and some of this money is given to their employees. Saying the money given to the government is on behalf of the employee or the employer is mostly irrelevant. There are cases where it is relevant if the employee or employer can get tax refunds against the money but mostly it is irrelevant. Who actually pays the burden of tax is a question of tax incidence (https://en.wikipedia.org/wiki/Tax_incidence). In theory the burden of income taxes could even be falling on your employer. But it is very likely that most of the burden of income taxes/payroll taxes falls on the employee. But if you are doing cross-country comparisons its much easier to just total up all taxes related to employment in one bucket and compare them under the assumption the incidence burden would be similar across different countries.
I think when doing casual person-to-person comparisons, like on here, it is actually easier to compare payslips.
Most importantly, I don't believe that if employer NI went away tomorrow that money would come to me in increased salary. Including it as a tax on me makes the assumption that it would.
I don't believe that if employer NI were removed that money would come to me, so I don't personally see it as unrealised salary, but that's just an opinion.
Employee NI went down by 2pts last year, employer NI is going up by 1.2pts this year.