"They" as a gender neutral singular pronoun is, to me, perfectly natural. I use it dozens of times a day as such without noticing.
Spivak pronouns, on the other hand, are blatantly marked, and were I to come across them in writing or speech, I'd find them very distracting.
I guessed - correctly - it would be the same Spivak who wrote the excellent Calculus textbook.
I agree that from a perspective of getting more people to use them the drawbacks are greater but from the perspective of understanding the drawbacks are essentially non-existent.
Another benefit that these novel pronouns can't pick up is that _they_ is the normal gender-neutral pronoun in use by native speakers, and has been so for centuries. The Spivak pronouns are not. If you have to explicitly teach pronouns to adult native speakers, or if using a pronoun requires deliberate thought, then there is something wrong.
I can think of two drawbacks of the normal gender-neutral pronoun, but I can't see how they are solved by Spivak pronouns, in fact, one of them is much worse.
1) Some people think that singular _they_ sounds awkard. However, considering the Spivak pronouns are a novel coinage in a closed class of words, it's almost certain that more people would find them more awkward than the normal gender-neutral pronouns.
2) There is a possibility for ambiguity with the plural pronoun. However, I can't think of a situation in which it wouldn't also be ambiguous with an distinct singular gender neutral pronoun.