Sure, direct control means more influence.
But why do you think, that Italy could do more economically than pay a rather small italian field army?
Odoacer's force numbered 20-25.000 men when he faced Theodoric at the Isonzo and Verona for instance. Had it not been for the interevention of the Visigoths, he could probably have defeated Theodoric whilst besieging him in Tincinum (which he could thanks to a number of Theodoric's forces changing sides)
An army of 20.000 mercenaries is no laughing matter in late antiquity.
It can do more economically for the east. Plus, the extreme strain on the economy that Justinians conquests brought, and the destruction of Italy and Rome that came with it, won't happen.
On the other hand, the eastern empire will bleed considerably in its confrontations with the Goths, who would still be in Thrace.