I had the intuition that the spaces strictly decreased ambiguity, but your point makes me really unsure of this. But written German already distinguishes nouns

I had the intuition that the spaces strictly decreased ambiguity, but your point makes me really unsure of this. But written German already distinguishes nouns from verbs with capitalization; can the grouping problem be made worse by spaces in the absence of ambiguities about which part of speech a word is? (Obviously the German convention doesn't totally eliminate all such ambiguities, since "wie" 'like (preposition)' and "mögen" 'like (verb)' are both lower case, although "Fliegen" 'flies (insects) and "fliegen" 'flies (verb)' can be distinguished sufficiently to remove the specific kind of ambiguity present in this particular sentence even if "wie" and "mögen" were homonyms.) (corrected thanks to commenter below!)