OP: "...I thought the perfect level panning was needed to make merging easier,..."
Yes, it will make the merging easier, but, in addition, if you also have the horizon going through the middle of the frame, then after the default merging, the horizon will be very close to straight, not substantially curved as in your image. If the horizon is close to being centered, this means that the geometry corrections to straighten out any slight remaining curvature will be less and won't eat away at your resolution as much.
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OP: "...But... maybe I should do a lens correction to the image before merging?..."
Not doing a lens correction before merging didn't cause your curved horizon. However, it always helps to do it because the lens distortion correction and the lens vignetting correction (the two components of the lens correction), will take some of the work off the stitching algorithm, probably produce a higher resolution result (after the horizon is straightened), and reduce any brightness jumps at the seams in the composite between one component image and the next. So, yes, it's a good idea.
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OP: "...Does Photoshop's feature do that? I would think so. ..."
Sorry, but I am pretty sure that PS's stitching tool doesn't do that automatically. Run each component image through either ACR or LR before handing them over to Photomerge or a 3rd party stitching tool. However, if you apply any other efx (eg, color balance, brightness or contrast adjustments, sharpening, etc.) to the images in ACR or LR in this process, make sure that exactly the same settings for these effects is applied to all of the component images in the set.
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OP: "... The horizon was not undulating. It was a neat curve...."
I didn't say that it was. What I said was, "The problem of curved, or even undulating horizons, ... is very well-known to people doing panoramas."
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OP: "...Do you mean the tools are better at stitching together with the desired perspective to begin with, as opposed to having to clean up after Photoshop's Panorama Photomerge? When I read up on software, Photoshop built-in was one of the top choices! I guess it got points for "easy to use", and I want something with all the knobs and buttons to play with...."
Yes, although I haven't done a personal comparison of PTGUI in the last couple of years, if you will look at last link in my previous post, http://www.johnhpanos.com/horizons.htm , you will see that it has a "t2" control point tool (and many features to support it) explicitly for the purpose of ensuring straight horizons.
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OP: "...I tried using "Arrange" (only) on the same set, ..."
This was a useful exercise. In particular, notice that the horizon in each of the component images that can be seen in your "arrange (only)" view is about 2/3rd the way towards the top of each frame instead of half way up, where it should have been, and the result of this was that when they were assembled into a panoramic composite, this produced a curved horizon that bowed upwards at the center.
BTW, notice that the last link in my previous post (referred to above) intentionally did exactly the opposite of what you did. For demonstration purposes, he intentionally and incorrectly placed the horizon in each of his component images only about 1/3rd the way towards the top of the frame, not at the half-way point. This was (a) to show that the default composite would be curved upwards at the ends, not at the center, and (b) that it could be corrected using the tools provided in the software he was using, PTGUI.
HTH,
Tom M
