I will not believe a policy based around future increases in carbon price unless it is implemented at a constitutional level (i.e. hard to reverse), comes with a detailed plan to redistribute the taxes raised in a manner that makes it socially just, and includes detailed information campaigns what the future price means for investments done now.
Having a huge carbon price in 10 years, for example, implies that internal combustion engine cars are worthless then. Just trying to implement a policy to stop selling them in ten years already causes a huge backlash, the idea that there will be the political capital to turn all existing ICE cars into expensive paper weights that only the richest few can afford to drive is wishful thinking.
Carbon prices do have an important role to play, but for those situations where we need to transform large systems in our societies (heat sector, mobility) that are incredibly ingrained in the status quo, relying on market mechanisms that depend on a politically backed price does not seem feasible.