Right, and why not? The situation would be exactly the same in terms of how much money goes to employee and how much to tax.
But these arguments are always made with the implication that things should change, because otherwise what's the point? And in this situation, suppose things did change, and the tax rates were reduced: now the employee would get the same amount (they weren't paying any tax!) and the employer would get more (they were paying all of it!). And if this applies when the employer pays all of the tax, when it's perhaps obvious this part of the tax burden wasn't the employee's money, it applies when it pays part of it.
(Of course, reading the thread again, this depends on what the definition of "we" is...!)
If I pay €X in tax, I can recover some of that money via tax deductible expenses. If my employers pays that tax, I can’t deduct anything.