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I don’t think that it is possible for Ethereum to have fees similar to Binance Smart Chain while it is working on Proof-Of-Work. Actually, I strongly believe that transaction fees will be lower when it is switched to Proof-Of-Stake. But I don’t think that Ethereum is likely to be as cheap as Binance or Polygon one day. Personally I prefer using BSC in any case. Moreover, there is a big ecosystem as well.
I think the transaction fee won't be lower even if it switched to proof of stake.
As long as there are some platforms that continuously using high gas fee with high transaction volume, the fee will stay high,
and we must using high gas fee as well so our transaction will be picked up on the network.