Earlier quoted context omitted.
If the costs can be passed on, then there is potentially no incentive to innovate, either. It might also still be more cost efficient to innovate less to reduce costs than to actually innovate to reduce costs. Predicting where these things go is quite tricky.
But if the costs can be passed on then that’s a means for emitters to differentiate on cost. If manufacturer A emits more and passes the tax onto the consumer, manufacturer B can undercut on them on price if they’re more efficient. Right now there’s minimal financial benefit to being more carbon efficient. If anything it’s disincentivised because efficiency is itself costly, so it’s cheaper to just emit.
But only if undercutting isn't too expensive/pays back fast enough. The issue is that from a revenue perspective things always look simple, from a profit perspective it gets more complicated, especially if things have switching costs/limited fungibility, are oligopolies and other structured markets. It might work like you outline but I would not be surprised if there are a lot of unexpected or undesirable results, too.