If you bought a gun primarily for recreational Sporting Clays doesn't make more sense to pattern at 25 to 35 yards and examine the pattern than patterning at 40 yards and labeling IC, Mod, F?

Yes, it is best to pattern at the distances that you normally shoot. You will find that you have little need for full choke on most sporting courses and IC/Mod will work in many places ot LM/Mod if it is a longer course.

It's good advise. Though I ran into an interesting situation while trapshooting. I shot one weekend at Leadville, CO. I was at 27 yards at that time but in Leadville I was lucky to hit a target or two. After the shoot driving down the road I realized the problem: I had the choke in the gun that I usually use at 2500 feet altitude in AZ. Leadville club is at 10,000 ft.! So it's fair to say I was not right on with my K-80 "rifle" that weekend.

How do you explain the difference between the two elevations and what is the remedy?

When I retired to 5380’ I learned quickly that the higher the elevation the less choke I needed. Phil Bourjaily gives the basics here:

https://www.fieldandstream.com/how-high-altitude-and-air-density-affects-shotgun-patterns/

At 100,000 ft.the thin air offered considerably less resistance to the shot and pattern than 2500 ft. The remedy is to open up the choke. When I would travel to Florida to shoot from Arizona I found I had to tighten my choke and pattern to compensate for the lower altitude and extremely humid air compared to Arizona. In that case it wouldn't be much, but when shooting all those registered targets you notice the difference. In Colorado I had already left by the time I realized what the problem was, so have no idea how much I would have had to open the choke.

By the way, as mentioned in the above article, humid air is less dense than dry air so you shouldn't expect more open patterns in Florida from humidity (altho effect of humidity on density is relatively small).

Back to the OP's question ........

I have a bit different philosophy on chokes for sporting clays. I use the choke needed for the longest, on edge, presentation I can possibly encounter. And I use them for everything. It made a better shooter out of me. What that turned out to be for me is modified in both barrels. One of my best friends, and shooting buddies, disagrees with me about that ......... but then, he manufactures and sells CompNChokes and Kick's High Flyers.

I know what you mean , Stan.
I want smoke balls. Not gentle erosion of the clay.

The game has evolved beyond 35 yards. At least for highest level stuff.
They will probably have to lighten the loads if we start running out of room, lol.

People have gotten very good.

As a practical matter, I think the gun owner can pattern his shotgun at whatever distance he wants. It probably makes sense to get the bloom where it is most advantageous for the course you are shooting.

How they might accomplish that would take a bit of doing, but it is possible.

An interesting topic, although rarely a problem for us Brits.
My normal Pheasant shoot is 250 feet above sea level ...

Here in Santa Fe, I’m shooting at 7,000+ feet.
Opening the chokes by one choke (mod to IC) does make a difference.