I don’t see much difference. If ARB is burned, arb gains value and the amount of ARB that will go from Dao decreases again. As a result, payments are made on a certain $ scale. For example, need $100M and $arb is $1. Then you need to spend 100M $arb. If $arb is $2 then you will spend 50M $arb.
On the other hand, the collection of fees as $eth will create a second topic of discussion. What should we do with the collected $eth, should we distribute it to stakers, should we buy arb, should we buy $arb and burn it? There will be a lot of discussion. Instead, burning $arb is simpler and will contribute to the value gain and block to spend much arb from Dao.