Korean could serve as a point of comparison, as modern Korean is written mostly without Chinese characters (you could mix them in if you really want to, but approximately nobody bothers), but it does have spaces between words. And yes, when you have a highly inflecting language, "where do the spaces go" is a very nontrivial problem.

It's a bit easier for Korean as it has far more available syllables (so fewer homonyms), but you could easily imagine these languages making different tradeoffs and ending up in different places.