the umlaut is solved by placing an e following the umlauted letter; e. g., ö becomes 'oe.'

The umlauts evolved from the ae/oe/ue form.
In very old books the umlauts are not used at all.
Then there are some books where - to save space (paper was expensive)/work (assembling the letters to a line - Gutenberg ...) the letter e was put on the same piece of wood/lead as the a/o/u so it stood above the a/o/u.
Then, a bit later, the e got turned 90 degrees to the left, for line height reasons.
When the letters got smaller, the e of course also got smaller - and with the then popular Fraktur fonts, only two small short lines were left over ...

Thus using ae/oe/ue instead of ä/ö/ü is really going back to the roots of the umlauts ;-)