There is no real safety issue if you do a really good job removing ALL of the air with the displacement method. The challenge is in removing all of the air. According to J. Kenji Lopez Alt at Serious Eats, "Excess air causes oxidation that can develop into off flavors or promote spoilage."
The second issue is with the seal if the Ziploc bags. Generally speaking, these bags are not designed to withstand high temperatures, especially not for long periods of time. It is quite possible the seal will fail during a long cook, ruing your food.
You could certainly use Ziploc bags and give it a shot, there is no dooming reason not to try it. Before cooking your expensive brisket or whatever you're looking to do a long cook with, I recommend trying to overcome these two issues with something cheap to see if you can get rid of all the air and if the seal will last.