This was common for lute players in the Renaissance and Baroque periods. Lute frets were usually made of the same material as strings and were tied on around the neck, so adding an extra full width fret was not hard.
Of course being tied on lute frets were also movable, so they could also reposition the regular 12 frets instead of adding extras.
Instead of tying on an extra full width frets another common option was partial frets. They would glue a piece of string or wood under a specific string, to just give an option to play one note with either the regular fret or the more in tone little fret (called a "tastino" (plural is "tastini")).
In this video [1] Brandon Acker uses a guitar that his luthier friend was building that had not yet had the frets installed to demonstrate with lute style tied on frets some different 12 tone tunings, then demonstrates using tastini to improve specific notes, such as little fret on the G string a little before the first regular fret so that G♯ and A♭ can be different notes.
The tastini he uses in the video are simply pieces of string held on with a piece of tape, so quick and easy to add and remove.
Actually, I'm one of those people. For over 20 years, I struggled with playing piano because I would have to memorize a different fingering pattern for the major scale in 12 different keys. I knew the mechanical process of it, but it was hard to develop the muscle memory and play songs by ear based on intuition alone. So I was most comfortable playing in C major (white keys only) and using mechanical/electronic transposition.
In the year 2024, I stumbled upon the Janko piano layout ( https://en.wikipedia.org/wiki/Jank%C3%B3_keyboard ), which turns out to be the smallest modification to standard piano that results in an isomorphic keyboard. I kid you not, I was up and running in less than 5 minutes - I just treated the layout as if it was a pattern to learn on standard piano, except that it was the only pattern I ever had to learn. On Janko, I found it much easier to play songs by ear, in any key. I wish I discovered Janko earlier, as standard piano was never a good fit for my brain.
For anyone who is curious to try, here's a software Janko piano keyboard that you can play right in the web browser: https://novayashkola.org/janko/
As a side note, the traditional keyboard size is not representative of the average pianist's hand size. David Steinbuhler [3] has been making modified traditional keyboard layouts by varying the width of the keys slightly, and people rave about it. I've had the chance to visit his shop in Titusville, Pennsylvania, where he designs them. It's a totally enhanced playing experience, even for someone like me who can play a 10th without difficulty.
[0] https://en.wikipedia.org/wiki/Harpejji [1] https://dodekamusic.com/ [2] https://www.lumatone.io/ [3] http://dsstandardfoundation.org/the-standards/