NB, I can't tell you that I'm right and that you're wrong on this issue, comparing an antenna with and without a modest top hat, but I have experimented with the idea on an old AstroPlane before.
I couldn't tell any difference operating my radio for a period of time. I just took the top hat off and added a length of 1/2" tubing using two hose clamps. I tuned that length of the A/P until I saw a good match, and in this case the top hat was about 50% of the radiator not 20" inches...like is on the top of this I-10K. That was my only experience doing such a comparison. Even though I couldn't compare side by side, I did look back at my old signal reports at that time and found I was testing this A/P tip idea against my Sigma4 which was the other antenna up. There is not much value in these two reports for the purpose of our discussion, but hopefully it shows I did some work and not just providing words.
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Then later when I started modeling I made such a comparison, and noticed similar results with both antennas showing almost identical performance, like I posted above and have posted before. I didn't recall the resulted showing a difference in maximum TOA angle, and favoring the full length 1/4 wave radiator, but I doubt those models were only 18' feet high either, and height might make some difference.
I know these words might not be convincing for you, but this is what I've done trying to figure out...if using a top hat influences performance or not.
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I'm surprised you don't even consider the Current Report showing wire #3 for both antennas, showing an obvious increase in the radiating part of the radiator on the top hat model. Remember, the same principal we have here is used to try and explain why a 5/8 wave antenna produces a better signal than a 1/4 or 1/2 wave...by raising the current distribution.
Your argument that the overall currents/voltage should be the same, may or may not be considered descriptive of what is going on here. After all, modeling software uses a controlled input in the NEC engine, maybe 1 amp, so what you say is true to the fact, but you're ignoring the actual current distribution also provided. This same principal is used to describe mobile base loaded vs. center and top loaded antennas.
Don't you get it?
NB, I may be wrong in some areas because I think and consider the ideas, but I didn't make this stuff up.
You also comment about the lower portion of the radiator where some of the currents are out of phase, wasted and minimize of any useful radiation in that area of the radiator. That is true. However, you didn't notice, in this important lower area of the antenna we have to consider that the top hat model shows less currents flowing per segment. I consider this like adding current to the top section of the radiator that is really useful in radiating our signal in a positive way.
All this said over an issue for me, that on balance,
makes little difference in performance, in theory, and my real world experience. You on the other hand seem to be claiming some
notable advantage is to be expected... using a full length radiator instead.
I guess we'll have to agree to disagree.
Have you tested such and idea in some way?
BTW, let me note, that the top hat model is 263.25" tall without including the top hat, and the full length model is 284.25" tall, with the matchs for both showing to be similar. So, the top hat is consider to be a physical 20" top hat, and you add 5% for the electrical length approximately. I just thought maybe you'd like to know that.