The goal was to use only basic latin letters. But even then - many Slavic languages use or used z for this purpose, none uses x. So why make it arfitically less understandeable? It's not Cxechia it's Czechia.

why not sh, ch and zh then?

In some slavic languages "sh" and "ch" already exist. In fact in Czech "ch" is considered a single letter

Historical baggage. The 'c' doesn't contribute to the sound of the czech 'ch' (russian 'x'), unless you read the 'c' as an english 'k'. Kh as in Kharkiv makes more sense.

Slavs don't use these AFAIK but that would also be preferable to sx etc.

Bulgarians use those when transliterating bulgarian in thr latin alphabet

TIL that this is called Gaj's Latin alphabet [1]

[1]: https://en.wikipedia.org/wiki/Gaj's_Latin_alphabet

Isn't that like only 2-3 out of all Slavic languages and not the biggest ones?

Also, it would just make it harder to type on current layouts.

True. I don’t know much about other Slavic alphabets (other than my own, Serbo-Croatian). It looks like Polish has ć, ś, ź for this purpose. I’d be interested to learn more about the alphabets in Cyrillic. I assume they also have special letters for these three phonemes.