In 2v2 battles it gains a new purpose:assistant. Any Eevee can have Helping Hand, and when partnered with another Eevee, it can deal devastating damage.
Umbry can be partnered with Espy and have Helping Hand, Mean Look, Charm, and Wish/Moonlight. Charm is there to cover Espy's low DEF while Espy sweeps everyone. Mean Look keeps the Charms in place. Helping Hand makes Espy's 00ber Psychic even better. Moonlight/Wish heals Umbry to keep it alive to do the same assist on other Eevees and other low DEF sweepers.
Espy/Umbry vs Snorlax/Skarmory
Espy uses Reflect.
Umbry uses Charm on Snorlax.
Snorlax uses a now wimpy Body Slam/Return on Espy.
Skarmory uses Spikes.
Espy uses Morning Sun and recovers to full health.
Umbry uses Mean Look on Snorlax.
Snorlax uses a wimpy Body Slam/Return on Espy.
Skarmory uses Spikes again.
Umbry uses Charm on Snorlax.
Espy uses Morning Sun.
Snorlax counters with a very wimpy Return.
Skarmory use Spikes a third time.
Now attack with assisted Psychic. It has no power to kill you with so you have all the time in the world(plus three more Morning Sun PP). Umbry might Charm it again, and without Fire Blast, it has no power.
This is a specialized battle scenario, created by me to illustrate the potential power of this partnership. Espy has the e4 Espy moveset, Psychic, HP Ice, Morning Sun, and Reflect.