That wasn't the problem. It was that it really was a type setting machine.
The Mergenthaler Linotype is a type casting machine - it casts metal slugs with one line of text. The brass matrices from which the type is cast are reused within a minute or two. The matrices have a set of binary coded notches on the top which allow them to be sorted automatically.
With type setting, you don't get the letters back until you're done printing, and so you need huge supplies of type, which has to be sorted after use. Linotype slugs just get melted down for the next go-round.

Here's how a Linotype works.[1] There are more popular videos, but this training film gets across how the machine really works.

The article mentions the Linotype being slower than the Paige compositor. That was
probably true of early Linotype machines. Later machines added more concurrency.
From pictures of the early machines, it looks like there's only one assembly and casting station. The typist could get ahead of the caster and have to wait for it to finish. That was quickly fixed once they had some operational experience. In
later machines, it's an assembly line - the matrices are assembled into a line, moved to a holding station by the assembly elevator, and then moved to a casting station when the caster is free. With that buffering, the typist doesn't have to wait for the caster.

Roughly the same design was used for over eighty years, with only minor changes.
Which is surprising, considering how bulky the machine is and how clunky the design looks.

The only real competition was from Monotype, which also made a line caster, but with a completely different approach.[2] Monotype machines have a keyboard and paper tape punch as the input device. The caster, a separate machine, has a paper tape reader. It's more compact than a Linotype, but the caster, which casts one character at a time, is slower, at about 3 chars/second. So a big shop might need more casters than keyboard units.

Amusingly, the Monotype caster reads the paper tape in reverse. This allows the typist to "backspace" and cancel the previous character or line from the keyboard, since the caster sees the cancel before starting work on the line. On a Linotype, to correct an error, you have to finish out the line (this is where ETAOIN SHRDLU comes from; if you run your fingers down the keyboard vertically, you get that), wait for the caster to finish the slug, then discard the slug.

These machines belong to the small set of very complicated but mass produced machines of the mechanical era. Very few people could do design like that and make it work. A few examples:

- Howard Krum - Teletype machine (1920s)

- William Burroughs - adding machines (1895)

- Joseph Brown - automatic screw machine (1865)

There may be a few more, but it's not a long list.

Excellent mechanical design is a rather rare skill.
Most of the mistakes made by bad programmers have been made in mechanical design,
but in metal they are more visible. They show up as high cost, low reliability, too many
parts, excessive wear, a need for too tight tolerances or expensive materials, and such.

(I restore 1920s-1930s Teletype machines as a hobby, which gives some insight into
what works in mechanical design.)

[1] https://archive.org/details/0066_Typesetting_Linotype_02_25_...

[2] https://www.youtube.com/watch?v=r8jP91XowAE