Idk, I still wouldn't do it, the reason saltwater works without a filter (I still run one in mine regardless) is because your live rock builds up bacteria colonies that break down the waste.
Your plants aren't going to break down waste into usable nutrients, they're just going to use them, but if there's nothing to grow bacteria on to break down the waste it's just gonna build up and look nasty.
Now there should be some bacteria in your substrate, but this isn't really an efficient place for them to colonize in large numbers, so it would work to have no filter if you had incredibly low stocking in livestock, but still I'd just have a filter and more fish.
You're forgetting the immense surface area within a planted tank; all those plants. bacteria grow all over them. water flowing over their leaves is being filtered/cleaned all the time. Think of it as a symbiotic relationship between some coral and the algae that grow on them.