No, I am currently using a TubesZB Ethernet controller, but before that I used a Deconz ConBee II. There are others available as well.

I used the hue bridge before setting up HA, but after setting up and configuring the other controller, you can unpair your hue bulbs from the hue bridge and pair them with the new controller instead. You can then unplug the hue bridge, because the new controller is now handling the hue bulbs.

This is possible because devices that comply with the ZigBee protocol specs must accept properly formatted commands from a hub/controller after a successful pairing.

So if you have one of these controllers, AND the ZigBee device you purchase is compliant with the protocol AND the device is supported by the controller, the controller will be able to control the device locally, and you can throw out the "required" hub from the manufacturer that sends your data to that company's servers. This is why you need to plan things out ahead of time, to ensure that what you get will work with what you have. Every controller has a list of what devices are supported. For example, here are the devices supported by the ConBee II, and here are the devices supported by the TubesZB device, which uses Zigbee2MQTT.

Bonus: with one of these controllers, your smart home stuff will now work just fine if your internet goes out. As long as your local network is up and running, all of your HA stuff will work as well.