Kakashi isn't spending his own chakra, he's using the chakra he received from Obito. Hagoromo was able to permanently grant Naruto/Sasuke half his power... Obito can temporarily grant Kakashi his power. Apparently if Obito's full chakra is transferred, it includes the Sharingan, which are nothing but a manifestation of Obito's spiritual energies.
Obito returned to reality using his spiritual energies, I.e. Kamui (Sharingan power = Spiritual). Parts of his body were still present, and they acted as a tether to let his chakra return from the Pure Realm (similar to how Edo tensei summons a soul from the Pure Realm and tethers it to a corpse). Like Edo Tensei, the summoned chakra can recreate Kekkei Genkai.
Kakashi is spending all of Obito's chakra at once, hence why he can achieve a complete Susano'o.
Obito returned to reality using his spiritual energies, I.e. Kamui (Sharingan power = Spiritual). Parts of his body were still present, and they acted as a tether to let his chakra return from the Pure Realm (similar to how Edo tensei summons a soul from the Pure Realm and tethers it to a corpse). Like Edo Tensei, the summoned chakra can recreate Kekkei Genkai.
Kakashi is spending all of Obito's chakra at once, hence why he can achieve a complete Susano'o.