> If the employer didn't have to pay those 31% to the government, he would have paid them to you, and you would have been taxed on them.

It's unlikely the employer would pay you more. You negotiated and expect 10,000 SEK. Yes, the employer knows it'll cost 13,000, but you only get 10,000. So if there's no employer tax, you'll still likely get 10,000, but now the employer can hire another person using the money that's freed up, or invest in some other ways.