These aren't homonyms. The tones are different. They are as easy to tell apart for native speakers as different vowels or consonants. You may find tones mysterious but it's only because Russian language isn't tonal. Vietnamese, Laotian or Thai native speakers will find Mandarin tones very simple.
Tones aren't something special. Almost half of languages in WALS are tonal. And I'm sure there're tonal languages missing in their database, like Limburgian and Central Franconian. Tones are important partly because they encode grammatical information. I'll keep using the 咽 example: if it's pronounced yàn, it's a verb meaning "to swallow". If it's pronounced yān, it's a noun meaning "throat".