I heard that
trustedcoin (the 2fa service used by electrum) is not free and charges you a small fee too.
The fee you pay to trustedcoin will be small only if you make transaction from your wallet regularly.
They offer two batches of 100 and 20 transactions.
As stated in the link you shared, you must pay 0.0005 BTC for the batches of 20 transactions and 0.00125 BTC for the batches of 100 transactions.
This fee will be charged in the first transaction you make from your 2FA wallet.
For example, if you make only one transaction from your wallet and then disable the 2fa and don't use that wallet for any reason, you have to pay around $12 dollars worth of bitcoin only for one transaction.