To reframe the analogy: carbon pricing allows drivers to decide for themselves whether it is more cost efficient to speed and pay a toll. 
I think youre missing some aspect(s). Some companies will reduce emissions more than others, that is true. Under a cap-and-trade system companies that can reduce their emissions at lower costs will do so and sell their excess pollution rights. Companies who cannot reduce emissions as efficiently may then want to buy those excess pollution rights. Each party is acting in its own interest and the price of those pollution rights is simply determined by the market (and, well, the cap). 
The reason cap-and-trade will effectively reduce emissions is because of the cap. One cannot infinitely buy pollution rights; there are only a finite amount of them. That is a key difference between cap-and-trade and a carbon tax. With a carbon tax the gov (not the market) puts a price on pollution rights and there are technically an infinite amount of them. In both cases companies are incentivized to reduce emissions to the point which is most profitable for them. The goal is to achieve the necessary emissions cuts at the lowest overall cost to the economy.
Well past efforts to reduce emissions have relied on carrots in the form of subsidies and tax breaks. With a revenue neutral carbon tax the carrot would be equal cuts in capital gains taxes, payroll taxes, income taxes, or something else. We could scrap those old subsidies and tax cuts entirely, both for fossil fuels and alternative energies. There are many options. These options have been on the table before. We just need a certain group of politicians to come to the table to have these discussions.
Instead...
Jim Inhofes snowball has disproven climate change once and for all