There is a lot of information on this forum about what chickens have to have in a nest. I personally don't believe most of those are absolutely necessary. I grew up on a farm. One of my chores was to gather eggs. Most of those came from the henhouse but some hens would hide a nest, often in a hay barn. It was my job to find those. Some were out in the open, wide open. No cover that I could see at all. Some were well hidden in pretty tight dark areas, much smaller than the common minimum size of 12" x 12" x 12" that you often see on here. I don't know why some of those hens chose to lay where they did. I'm sure they had a reason.
Did you know a hen raises up to lay an egg? The egg comes out of the same vent the poop does but they have different plumbing inside. To seal off the poop from the egg so the egg stays clean, part of the egg-laying plumbing sticks out maybe 1/2" to seal off the poop section. Since the hen does not want to get trash on that 1/2" that sticks out she raises her rear end up off of the nest a little. A 12" high nest is plenty for her to do that. She doesn't have to spread her wings, stand up and reach for the sky, just raising her butt a little is enough.
By instinct a hen should know to not poop in her nest, at least not when laying an egg. Another chicken might go in there and poop, but not one laying an egg unless her instincts are warped. That sometimes happens.
I've had success training a hen where to lay but you have to be around at the right time. I made some of my nests so I can lock a hen in them if I want to. That lock has come in handy for a few different things. When a hen decides to make her nest somewhere unacceptable to me, I catch her when she is on that bad nest and lock her in the right nest until she lays that egg. Usually a half hour is enough but one hen took 3 hours. Usually just doing that once is enough to retrain her but I had one that I had to do two days in a row. But you have to be around to catch them on that bad nest.
Some people handle it the way you mentioned, just accept that as an OK nesting spot and maybe put a nest there.
I've never tried this but some people say they have had success by putting a nest where they are laying, maybe a box or milk crate with bedding. Leave it there for several days so they get used to using it. Then gradually move it a foot at a time and waiting a few days to move it to a better place. If you get them to some place acceptable, you are gold. If you really want her to use your real nest, get her used to that immediate area then remove the temporary nest. She might decide to lay in your real nest or she may find another place to lay.
I believe that if it isn't broken, don't ix it. It's up to you to decide if it is broken or not.