I don't use Control4, but I do use an automation system at my house. I also use
BlueIris for my cameras. I use MQTT to integrate the two systems. BI has excellent trigger functionality built in and MQTT is one of the output options, so as long as the automation system can react to MQTT commands, it is really easy to integrate the two systems.
That being said, I only have one scenario that I've integrated. I have the system turn on my front porch light if: it's night, the front porch is currently off, and the front porch camera triggers from motion (camera based AI trigger on "people"). It turns off again after 5 minutes if the home alarm is armed night. Obviously I could accomplish the same thing with some sort of motion floodlight, but honestly this was easier and visually more appealing.
I really cannot think of any other scenarios that are important to me. Obviously one would be to set a BI profile based on the alarm status. For example I might record only outside cameras when the alarm is disarmed, and inside and outside cameras when the alarm is armed, but I don't have any inside cameras that I don't want recording 24/7.
I'm curious to hear what scenarios you see yourself integrating the cameras into the automation system. Maybe you'll have an idea that I haven't thought about!
EDIT - I will say that I have the CCTV cameras showing on my automation GUI. That's just using streaming ip addresses however, not really "integration" in my opinion.