It's not in principle an insane idea, but it's got problems.
In the UK, comparatively few people actually complete a tax return, the tax is deducted at source - 'pay as you earn'.
This works well for people in stable employment - it 'just works', and they don't need to do anything.
However - it was started in 1940 or so - and employment is a whole lot less stable now.
For people with more than one job, or who move employers lots, it can be tricky, and doesn't work well, leading to refunds or underpayments of tax.
The above proposal would in principle make it easier for employers and employees.
It's got the obvious problem that if you have a problem with your wages, you can't go and shout at your employer.