Having sequencers set their prover prices ahead of time requires them to have sophisticated market pricing information. This causes centralization pressure.
Having sequencers pay the proverDeposit means they have to run their own auction. This is a sophisticated activity, and causes centralization pressure.
Requiring two L1 txns from sequencers will exacerbate the Fernet L1 gazumping problem.
Because the prover has nothing at stake (in-protocol), the cost to bribe them not to produce a proof is only Edit: This will be handled by the sequencer during their auction as a sophisticated activity.proverTip + proverReward, rather than the desired proverDeposit.
You have to burn it, otherwise colluding sequencers can reorg for less than proverDeposit.
This would create centralization pressure on sequencers.