The premise of collective bargaining is that workers join together to bargain against their bosses. For public sector employees, the bosses are the taxpayers. The bosses are not government representatives.
To have the unions negotiate with government representatives is ludicrous, because in the real world, those government representatives in fact stand for the unions against the taxpayers.
If we are going to have collective bargaining in the public sector, we need the taxpayers represented in a way that they presently are not.