Human form lets him shapeshift. It says so in the description of the power in the first line: “you’re a shapeshifter”
For instance, let’s say he’s a crappy fighter with a fist score of +1
When he shape shifts into a dragon form, he’s still a crappy fighter. It doesn’t imbue him with any instinctual ability to bite or claw someone.
If he takes beast shape, the instinct kicks in. Now he shuffles his skill tree to move fists to +4.
Human form can be used for anything. It assumes you are in a Human Form with no powers. You could, for example, be an angelic scion.
You take human form and attach Inhuman Speed and Wings to it. This represents your ability to sprout wings and fly around. There’s no need to take beast shape.
In fact, shape shifting could be completely narrative with no powers attached to it, as long as you have an aspect that can be compelled or invoked.
He definitely should have an aspect tied to human form. It’ll probably be his High Concept. You are the GM so if you think he should have beast form, then that’s your prerogative but it certainly isn’t necessary. The character will be way more useful if he takes beast form though.
The question you should both be asking is, will beast form fit the character?
Is he a dweeb that isn’t comfortable in his shifter form? Then low fists and no need for beast form. Is he a pro fighter that enhances his fighting abilities with claws and scales? Then high fists and no beast form.
Is he a social butterfly who lets his inner dragon sometimes take over? Then He should max his social skills, take beast form and reshuffle his skills when he’s fighting.
Maybe he’s a super perceptive private eye who uses his dragon form to protect himself, then he can max alertness and investigate and take beast form for the skill shuffle.