Wells Fargo charges for payment transfers to other banks, but does support no fee Zelle & PayPal. We get around this by using a different bank to initiate a free transfer to or from WF. We still have the WF account for local services (free notary) but keep just enough in it to support recurring EFT transactions that charge a fee for using a credit card. We also link PayPal & Zelle to this account to keep our exposure minimal; we use them for payments with friends who prefer this method. We never write checks anymore against WF or use its bill pay.
Our primary checking account is Schwab: no fees, free checks, ATM fee reimbursement anywhere in the world, bill pay that withdraws our money only when the recipient cashes the check, mobile deposit. In addition to no fee for transfers, it has a high $100K limit on daily transfers. We also have savings accounts with Ally, Synchrony, & CIT (linked to Schwab) but never do Zelle with them.