Poetry is the marriage of prose and rhythm, which makes it particularly powerful a tool for either mnemonic devices, or pathos, or both. Good poetry is powerful and striking, and it is neither better nor worse than a piece of prose well-done; it is a complementary genre.
Poetry is treated as a form of literature that can tell us more than what reads the eye. But as any school kid would argue, why do we have to analyze and dissect a poem to understand it?
Because teachers are trying to ingrain the little troglodytes with the skill that comes naturally to a person of erudition, intellect and taste: the ability to read between the lines. Since your garden variety protozoa cannot be trusted with this, teachers around the world try to provide the tools to correctly decipher poetry by letting their students exercise line-by-line.
A doomed endeavour, given the average hay-for-brain's intellect.
Why do poems hide their meanings
They don't; they just express them by means of circumlocution, so as to convey additional information that would difficult, impossible, or uninteresting to render by way of prose.
and are their meanings even worth while?
That depends on the poetry.
So ask the poet, "Why the hell can't you just tell me what you're trying to say!?!"
Hear ye indeed, but understand not; and see ye indeed, but perceive not.