I don't really think there is a point, other than the small friendship boost to a few random campers currently present at your site, and the "upgraded" look of the amenity.
I hope this reply will answer this monthly-returning question. Because of aesthetics.
The max-upgraded amenities all look different from their Lv1 state. The best example is the natural picnic set. The max-upgraded version just looks better, with more fancy details.
Aside from their looks, when you are crafting 3rd tier amenities you'll probably have reached max capacity on certain materials at least once. If you have the materials, why not upgrade? It looks better, it shows other players you are active, and I see no reason why Nintendo wouldn't choose to release a 4th tier amenity in the future.
I didn't see the difference in asthetics on the tier 3 amenities, and on a few of them they look exactly the same to me. Sorry for asking, I didn't see that anyone else has posted this question, monthly or otherwise, it seems this section of the forum is dying out. Next time I will be sure to go through every thread before posting a question.
You can go into the craft screen or the catalog and hit the button to switch between the two versions. Not all of them are really obvious. For the merry-go-round, I can see that the final version has balloons, but I had to take screen shots to really note (small) differences in color. Others are way more obvious, like the pool.