BNB's gas fees are increasing simply because the network is starting to experience congestion. ETH used to be cheap, but that's not the case anymore due to high network load. That's the problem when a blockchain network becomes too popular in the mainstream world. It's up to developers themselves to roll out network upgrades in order to keep the blockchain as cheap and fast as possible.
It happens with many networks. Fee is cheap when price of coin is cheap and the network is not congested. Network usually becomes congested when price soars a lot and besides that there are increasing activities on network.
Ethereum had some periods like that with ICO in 2017 and DeFi in 2020. Binance Smart Chain is facing congested issues with more demand from NFT marketplaces, GameFi projects and more.
If by any chance BNB's fees become exorbitantly high, people have the choice to switch to other competing chains.
AVAX is a good chain to be alternative for ERC-20 and BEP-20 chains.