The ultimate currency in FATE is plot impact.
People sacrifice Refresh (potential free Fate Points) in order to gain a consistent, pre-established means of impacting the plot, such as Spell Use, Claws, Toughness, or Speed. As such, it is easy to rationalize that when Shapechanging, your ultimate goal should be to actually *get* the powers which make sense for that form.
But Aspects and Fate Points are still mechanisms of plot impact, and if you are able to negotiate with your table that a Shapechange spell nets you a bunch of taggable Aspects, and not just a suite of Inhuman Abilities, with the understanding that those can be tagged for certain benefits and plot impact, then great.
And if you really just need to have the Inhuman Abilities, then there is a mechanism for it!