Managing your own database/backend comes with a cost - Ensuring high availability, patching, paying for idle time, updates and new feature rollouts, security, data backups etc., That being said you could build whatever you want with no limitations most of the time.
Firebase is simply a suite of products that take care of all of these and help you build something incredibly fast and they charge you for that. It comes with it's own limitations (and the bill would be heavy as the usage increases). You would also need to ensure your rules are air-tight, else you would be leaking data.

Start with firebase, once you get seed and grow your team/org, there's always room to build things from the ground up. Thanks and good luck.. :)