You may not be able to avoid account fees completely, but you can certainly minimize them. Most brokers will charge a fee for transferring out funds or closing your account. If you’re transferring to another broker, that new company may offer to reimburse your transfer fees, at least up to a limit.
Most other fees can be sidestepped by simply choosing a broker that doesn’t charge them, or by opting out of services that cost extra. Common fees to watch out for include annual fees, inactivity fees, trading platform subscriptions and extra charges for research or data.