That's exactly what I needed, many thanks. The author there also discusses other rationales which he considers later invented excuses, not the real reason, then shows what he believes to be the original idea. Once having this I've also found a shorter summary by the same author:
"It evolved during the development of the machine later called the “Blower” Linotype, which entered production in 1886. In this machine, the magazine consisted of a set of rectangular tubes set vertically (and permanently) in the machine. Mergenthaler knew that he would need to supply matrices in varying numbers, and he knew the frequency of the letters (stories that he asked for a count to be done are dubious - typefounders and printers had known the letter frequencies for centuries). But he was worried that the matrices might be damaged by their fall through these vertical tubes. For the most-used matrices (e, t, a, …) this was not really a problem, since they were supplied in greater numbers and would tend to fill their tubes a bit more (limiting the distance of their fall). But for the less-used mats (supplied in fewer numbers) he feared a problem. So he arranged the tubes in decreasing lengths and put the most frequent characters to the left. The layout of the magazine-tubes led directly to the layout of the keyboard below them. We know this because he said so in US patent 378,798 (filed 1886-07-17, issued 1888-02-28): “… If long tubes were used with a smaller number of matrices at their lower ends, each matrix would acquire a considerable velocity in falling to its place in the tube. This would tend to lead to the mutilation of the matrix.” (p. 3)
In the 1890 machine later known as the “Square Base” Linotype, Mergenthaler introduced a different solution to this - the inclined magazine, which avoided matrix freefall in the magazine. But he kept the “etaoin” layout."
"It evolved during the development of the machine later called the “Blower” Linotype, which entered production in 1886. In this machine, the magazine consisted of a set of rectangular tubes set vertically (and permanently) in the machine. Mergenthaler knew that he would need to supply matrices in varying numbers, and he knew the frequency of the letters (stories that he asked for a count to be done are dubious - typefounders and printers had known the letter frequencies for centuries). But he was worried that the matrices might be damaged by their fall through these vertical tubes. For the most-used matrices (e, t, a, …) this was not really a problem, since they were supplied in greater numbers and would tend to fill their tubes a bit more (limiting the distance of their fall). But for the less-used mats (supplied in fewer numbers) he feared a problem. So he arranged the tubes in decreasing lengths and put the most frequent characters to the left. The layout of the magazine-tubes led directly to the layout of the keyboard below them. We know this because he said so in US patent 378,798 (filed 1886-07-17, issued 1888-02-28): “… If long tubes were used with a smaller number of matrices at their lower ends, each matrix would acquire a considerable velocity in falling to its place in the tube. This would tend to lead to the mutilation of the matrix.” (p. 3)
In the 1890 machine later known as the “Square Base” Linotype, Mergenthaler introduced a different solution to this - the inclined magazine, which avoided matrix freefall in the magazine. But he kept the “etaoin” layout."
(From http://www.briarpress.org/40298 A comment by David M MacMillan on 7 Sep 14)
Now the only thing missing is the scanned "US patent 378,798" which seems to be too old to be accessible?
Edit: Found! https://www.immigrantentrepreneurship.org/documents/ottmar-m...