For the ribbon vibrator portion, they had to choose at least one key to check, and likely choose one of the repair person's favorite default alignment keys.
It's used in alignment because the capital H is both wide and tall and the lower case h goes above the midline which neither m nor n do. On serifed faces (especially), the HHHhhhHHH combination creates a pretty nice visual baseline to ensure the the type has the proper "motion" and is "on feet". These Hs at both ends of the platen and in the center help to check print evenness when doing the ring and cylinder adjustment. They're also useful when adjusting the level of the line indicator though other letters like m, n, z, and k aren't bad either. Letters like v and i are thinner or almost non-existent on the baseline in comparison.
They also frequently use the / character which extends both above and below most other characters to ensure proper alignment with respect to both a bichrome ribbon and the strike against the platen. You want a nice even imprint from top to bottom. % is also good for this as well.
Some of the repair manuals at https://site.xavier.edu/polt/typewriters/tw-manuals.html as well as some of Ted Munk's manuals available through the typewriter database describe many of these adjustments and suggest specific letters for easier visual inspections.
I'd be curious to hear other repair people's favorite letters and characters.
Incidentally, for installing ribbon, many but not all manuals will suggest putting the bichrome setting to red and then simultaneously pressing the G and H keys so that their typebars gently jam together just in front of the typing point. This raises the ribbon vibrator to its highest point and makes it easier to thread the ribbon into it.
reply to https://old.reddit.com/r/typewriters/comments/1ovt8ry/but_why_the_h_key/