It took me quite a while to change my approach to camping after 15 years of camping in tents and setting up for rain. We joked about hiring out to farmers who were experiencing drought because it rained EVERY single time we camped.
So rain was one of the motivating factors in moving to a pop up. Man, oh man! No rivers running between the sleeping bags, no wet duffle bags because they brushed up against the tent wall, etc. And a hard floor. Now we're talking.
I still wanted to set up the large tarps I have worked into a "system". It was always set up the tent, set up kitchen and eating area and then throw the tarp(s) over the whole thing.
As others have mentioned, if you have a maintained pop up, you don't need tarps over it. It doesn't necessarily have to be light-weight like a tent so it can use water-proof materials, not just water-resistant materials.
If you are getting water inside your pop up, something is wrong and you need to address it. Otherwise, open up the awning or bring a tarp to cover the picnic table, grab a chair and enjoy the sound of the rain as it bounces harmlessly off of you and yours.
And not to your point but to others, every manufacturer's instructions that I have read that addresses long-term storage says to not use a tarp but to use a breathable cover. Unfortunately, they seem to be made like a plastic paper towel and are flimsy feeling, but I wouldn't want to run the risk of using a tarp for storage. Only if the tarp is kept completely away from the surface of the pop up AND does not seal off airflow. I have seen some people who have basically built stick frames and covered them with tarps that they park the pop up under. I can see no problem with doing it that way.