I much prefer using the public washrooms for lots of reasons, many stated here already.
- If real early I don't wake the wife
- Lots more room
- No using my own water or filling my tanks
- More room in shower
- Always nice to go for a walk, even a short one
- I can often chat with other campers on the way there or back
- For my wife a longer shower to wash hair is much easier
With campground showers I only care that they are cleaned and the water is warm and has a decent pressure. I don't care if they are all modern looking. I must pick good campgrounds as I have only once or twice come across one I did not use. The biggest issue I have had is that I am often the first one in for the day and have to prime all the hot water pipes for a bit until the flow gets through to the shower head.
There is nothing wrong with using the trailer shower, especially if you are a bit shy in public. They do the job great. We do a lot of boondocking so to save water and grey tank space, we mostly sponge bath then which works great, but still do use the shower the odd time. I used very little water have no hair, but my wife has a lot of nice hair so uses a bit more water to rinse it out.
I would have to guess in our last Escape we have had for 3 years, with few hundred nights in it, we have used the shower probably 20 times at the most. To be fair, we do lots of 3-4 night trips so as we are camping we have no need to shower usually, just use a warm wet cloth for cleaning.