Burn raises asset-backing (which is the baseline value) exponentially indeed!
Asset Backing tax specifically puts BNB into the Asset Backing pool which is what controls the rising baseline value. The only way to acquire the backed assets is by burning your tokens, and thus the baseline value does not get affected as the amount of backing to tokens does not change.
Liquidity tax (only on sells) raises the Liquidity Pool, improving price impact.
Asset backing doesn't have any direct effect on the LP, only the baseline value.