You don’t need to do it every time; you only need do it once per application. It’s a privacy feature that prevents an application being able to record your screen (or use your camera/microphone) without your explicit knowledge and permission.
And frankly Zoom just works, and works well. What advantage would using a random site with an unheard of record possibly give you?
To give an example, I've tried to convert colleagues to use meet.jit.si instead of zoom. On macs to share your screen you apparently have restart safari and give it some permission (I think you even need to do it every time? ). The people who were using macs were quick to dismiss jit.si because of this, even though it's completely an apple problem.