It really depends on the language, but the main reason why syllabaries can be simpler in terms of mental load is because syllables (or moras, or something similar) is how humans naturally break down words in most languages. Consider that even in languages like English with a well-established alphabetic orthography, words are still routinely spelled out syllable by syllable.
However, phonotactics place some practical limits on that. If your language only has (C)V syllables with a fairly limited phonemic inventory - e.g. Japanese - a syllabary is small enough, and even if letter shapes for related syllables aren't consistent, is easy enough to learn. OTOH if you routinely have, say, 3-consonant clusters (as in e.g. the word SCRipt), you quickly get combinatorial explosion.
To some extent this can be mitigated by alphasyllabaries like Hangul, where syllables are clearly marked in writing but still composed of some more fundamental units. Still, you can only cram so many tiny elements into a single glyph that is still distinct. Hangul actually used to have standard syllable blocks for all combinations of three consonants in the onset, and those are already very hard to read.
However, phonotactics place some practical limits on that. If your language only has (C)V syllables with a fairly limited phonemic inventory - e.g. Japanese - a syllabary is small enough, and even if letter shapes for related syllables aren't consistent, is easy enough to learn. OTOH if you routinely have, say, 3-consonant clusters (as in e.g. the word SCRipt), you quickly get combinatorial explosion.
To some extent this can be mitigated by alphasyllabaries like Hangul, where syllables are clearly marked in writing but still composed of some more fundamental units. Still, you can only cram so many tiny elements into a single glyph that is still distinct. Hangul actually used to have standard syllable blocks for all combinations of three consonants in the onset, and those are already very hard to read.