Why do fees vary this much?
The on-chain cost of a withdrawal comes down to the network you use. ERC20 (Ethereum mainnet) gas floats in real time with congestion, and when the market's hot it can cost several times more, so it's usually the priciest of the mainstream networks. High-throughput networks like TRC20, BEP20, and Solana are usually very cheap, and L2s and side-chains like Arbitrum, Optimism, and Polygon run a good deal below mainnet too. Bitcoin mainnet depends on how busy the mempool is, and the Lightning Network is cheap and suited to small amounts. For the same transfer, picking the right network saves you the bulk of the cost — as long as the receiving side supports that network.
To understand what gas actually is and why withdrawing ETH costs so much, read what gas is and why ETH withdrawals cost more. To choose a network around saving on fees, read the complete guide to picking a withdrawal network, or get a direction from the cheapest network picker.
It doesn't go online, doesn't run a live estimate, doesn't quote a dollar figure, and doesn't call any API. All it does is tell you, by network, whether the fee runs high or low. For the exact amount, open Binance's withdrawal page and read what your transfer actually shows — on-chain fees change in real time with congestion.