privacy

The hard part about writing untraceably on typewriters is that they're relatively rare these days. When everyone used them, it didn't matter too much if people could tell you used a Remington Quiet-Riter because tons of people had a common model like that. Nowadays, just being able to use a typewriter effectively either (a) means you're old enough to have used one or (b) typewriters/vintage stuff is an interest of yours -- or now, maybe just someone interested in anonymity enough to learn. If someone could tell what model of machine you typed it on, that would narrow it down further, and (depending on what the inquiry is about) that may be good enough info for their purposes, given the rarity of using typewriters today.

• IBM Selectrics are by far the most common type ball machines and the balls were not interchangeable among brands, so someone would be able to tell pretty easily. Some fonts are rarer than others.
• Daisywheel machines had a few more manufacturers in addition to IBM. I think there are still aftermarket daisywheels that can complicate identifying exactly what model/brand of machine typed a letter.
• Typebar machines were made by tons and tons of manufacturers in the 19th and 20th centuries. Each manufacturer had a book of typefaces it offered, though they changed from year to year, and the differences among similar typefaces between manufacturers were sometimes very minimal.

Since these machines are electromechanical, rather than digital, it would be quite difficult to encode identifying information into the type. Other considerations: tracing the purchase of the typewriter, ribbons, and possibly repair/cleaning services to get it working.