I'm not sure - how arbitrarily setting prices introduces certainty? Today the Congress or EPA decides the price is X, tomorrow Republicans take the Congress and the presidency and appoint the head of EPA which drops the price to Y, then next cycle Democrats take the power and rise the price to Z, etc. etc. - where's certainty in that? I don't see any objective way of setting such taxes, and as such - any reason why they would be stable is the price is purely arbitrary and thus subject to political games.
Well it doesn't, no. IF you have stable government policies, than a carbon tax would be a predictable cost, where a cap would be highly volatile. Obviously if the policies are changing too, then you can't predict much of anything.
"I don't see any objective way of setting such taxes,"
How about: estimate the economic damage of a marginal kg of CO2 (external cost), and set the tax equal to that? [0]
As an order-of-magnitude guess: [total climate change damage] / [total CO2 emitted], both discounted to present dollars.