Banning this certificate or at least warning the users against using it WILL help a lot.
Each authoritarian regime is authoritarian in its own way. Kazakhstan doesn't have a very strong regime, especially since the first president resigned earlier this year. When people protest strongly against something, the government usually backs down. For example, a couple of years ago the government withdrew their plans of lending lands to foreign governments after backlash from ordinary people. If Kazakhs knew about the implications of installing this certificate, they would have been on the streets already.
If Firefox, Chrome and/or Safari block this certificate, the people will show their dissatisfaction and the law will be revoked.
Sometimes the people in authoritarian countries need a little bit of support from organizations to fight for their rights. I really hope the browser organizations would help us here.