Not quite that simple. You have to diagnose why they showed up in the first place and correct that. On our farm growing up thistle endured forever because my dad kept the pasture grass at 1" all year long, and that sat atop the heaviest damn clay out there. Another perennial spot was where the cattle constantly trampled the ground near the buildings.
Where I think you can just walk away from them is where you've got short term one time disturbances. One example is where you have a fire. Another would be after spraying a food plot. Now if you keep spraying a food plot, you're going to have them just keep popping up a foot or two over from where the last one was. A third is like what I've got going in this thread. I spread about a foot of clay from a pond dig in that spot to fill in a trench. That clay came with less than a half point of OM, zero oxygen, low calcium, etc.
After the quality thistle crop I just laid down, I've got fiber out my ears in that clay from the thistle roots. The thistle above ground has become thatch. The next crop can follow the thistle root channels down, and I'm throwing gypsum on this weekend. I put probably a 10-12 way blend of annuals and perennials on there. Not all of them will make it, but some do great in dead clay like ragweed, black eyed susan, chicory, plantain, white sweet clover, jap millet, flax, etc.