Hahaha, interesting question. My frined also asked: will ETH2.0 cause ETH price to drop

Here's my opinion: when ETH2.0 really goes live with POS and greater scalability, say 15,000 tps instead of 15tps, the market's transactional demand is 20,000 tps.
Currently: ETH1.0 15tps, the transaction price will be $10/transaction (example)
After this: ETH2.0 15Ktps, the transaction price will be $0.01/transaction (example).
But the number of transactions also increased, so the miner profit did not decrease. More precisely, this profit will go to staking forgers, because miners only exist in the POW blockchain.
Furthermore, since staking does not require investments in machinery, electricity, labor, transaction costs will be reduced further and the entire community will receive this value.
ETH price is only partially dependent on the cost of mining, its main driver is market demand. And I think when transaction speed & cost is solved, activity on Ethereum blockchain will explode, and so will the need to use & own ETH. Under this scenario, ETH price will continue to rise.