Why is the base fee burned?
EIP-1559 offers a solid explanation (bold added):
This ensures that only ETH can ever be used to pay for transactions on
Ethereum, cementing the economic value of ETH within the Ethereum
platform and reducing risks associated with miner extractable value
(MEV). Additionally, this burn counterbalances Ethereum inflation
while still giving the block reward and priority fee to miners.
Finally, ensuring the miner of a block does not receive the base fee
is important because it removes miner incentive to manipulate the fee
in order to extract more fees from users.
Miner was the term used in Proof of Work and means the validator that is the block proposer.
A little more information about why base fee is burned
EIP-1559 was proposed because first price auctions are inefficient. The base fee needs to be burned to prevent off-chain markets by miners that would circumvent the base fee and degenerate to a first price auction.
https://timroughgarden.org/papers/eip1559.pdf briefly explains 7th takeaway:
The seemingly orthogonal goals of easy fee estimation and fee burning
are inextricably linked through the threat of off-chain agreements.
In https://youtu.be/62UI3Js30Io?t=1935 Roughgarden gives an example of how a base fee of 90 does not prevent transactions that pay less than 90. Because a user and miner can have an off-chain agreement where a user who only wants to pay 60, on-chain they pay 90, but get refunded 30 off-chain by the miner.