There are at least several possibilities

1) People, who don't want to be affected by global warming. Right now nobody is affected enough to pay and it is too costly (estimates are $500/metric ton, while emission per capita is around 20 tonnes/year).

2) Captured carbon can be sold commercially for use in plastics industry, at some point it will be cheaper, than oil/gas extraction.

3) Carbon emission trading already exists, some companies even doing it voluntary, like Google. Direct air capture can piggy-back that system.