Is it ok to lower grade around a well head instead of raising it?
A Thousand to weld an extension , wow!
I agree that the well casing should be above ground. As long as the ground water doesn’t get within 1” of the top I would not mess with it. For example my last house the casing was at ground level. I was on the side of a mountain I dug the high side down a few inches then graded the low side away even with the heaviest rains the water flowing down the hill never got close so it was fine. It may have been ok but I would rather a little safety margin.
If you don’t have high water issues I would say it is ok. I would protect it so it is not a spot that a dog can pee on it. We always put wishing well structures there if not in a well house. One really neat one I saw had a artificial bolder over it it looked really neat for that area.
So if you don’t have high water issues I would not worry. If you do have water over the cap I would probably find someone else a bit more reasonable To extend the casing.