Licit

Yes it will take a while but it should last much longer, be protected better and make it even easier the next time. I fully detail my cars enough that a simple wash or detail spray wipe down will keep it looking great. Over time the car stays looking great.
By the way you don't really have to do little sections at a time, I know it always says that on the bottle of whatever but it isn't a given. I have been detailing for years and do large areas or the whole car and then go back and buff off. With ICE it actually makes it easier to buff off by doing the whole car so it has time.
The reason people mention dawn is that it that you'll know the wax will be stripped but yes there are other car wash soaps that will take wax off, they just may not fully remove it.