It is just a quirk of linguistics. heighth / highth was perfectly acceptable and was common until the 19th century. This is a common question in English linguistic circles and is a favorite fun fact on grammar blogs. Modern English height is a dialect variant which crept its way in about 1200 CE and eventually booted out its host, for unknown reasons. Some suggest there was something about the final /-h-/ in the stem which tripped up speakers. There are at least two more examples, but I am struggling to recall them now. I had thought "wight" was one, but that's not correct. Neither is "draught."

The word "height" in Old English is hiehþu, with the thorn (þ) making our /-th-/ sound. This is just the root heah "high" plus the Germanic abstract noun suffix -itha-. We see the same suffix in cousin languages of Germanic, like Latin -tatis, Greek -tet- etc. Old Norse hæð, Gothic hauhiþa.