No. It may gain on BTC significantly, but I doubt it will "take over." Eth upgrades done and BTC has upgrades coming too, and Taproot will give BTC the ability to complete with ETH for a lot of the projects that involve Smart Contracts.
we need to look how transaction in binance smart chain network if want to said bsc take over ethereum or not. if we talking about this , i am belive bsc already take over ethereum. bu unfortunately cryptocommunity ignore this indicator and most of them only analize based price.
I think low transaction fees cannot be a reason for BSC to replace Ethereum as the king of altcoins. Because there is a possibility that BSC transaction fees will be high when BNB prices are high. However, BNB has the advantage of a limited supply, so when BNB adoption is greater than Ethereum, the price of BNB is easy to increase.
check on daily transaction number either in bsc or ethereum and you will able identify which platform used by most project in crypto market now.