The fundamental idea of carbon pricing is that businesses right now have basically no disincentive to spewing out as much CO2 as they want, except possibly for angering a relatively small amount of people who care strongly about the environment. Why on earth would they voluntary spend the money to needed to reduce their carbon footprint? (unless they determine it is cheap enough to buy offsets or whatever to be able to call themselves carbon neutral for marketing purposes.)

This also means that development of sustainable alternatives is often slowed, as they will cost more at first, even if they happen to end up being less expensive in the long run (which is unlikely to be true in all cases, but which could potentially be true in a few specific scenarios).

But what are the alternatives? Simply outlawing burning of gasoline effective on some future date will be no more equitable.

Putting a strict quota system on companies would also cause prices to rise and be unequitable to.

I don't see any realistically implementable system that does not potentially cause prices to rise, and obviously rising prices on most goods disproportionately affects lower income people.

You showed up with the wrong sign.

We also have fairly big income transfers in many countries, making this a somewhat orthogonal question.