The carbon capture market NEEDS to have public funding/intervention to make it profitable.
Now, carbon capture will be important if we want to have a chance of undoing atmospheric CO2, but IMO, while now it the time to invest in research it's not the time to deploy. More public/government funds need to be pushed towards limiting CO2 output and eliminating sources of CO2.
The notion of carbon capture is much the same as having urine capture in a swimming pool. There is no way it won't cost more energy to remove than it produced when released.