Well it was obvious through events OTL that Justinian was a Genius, so if he had instead dedicated his time to something else he could do some pretty amazing things.
And if he left the empire in great shape after his death, later Emperors could make better headway in Italy and Reclaim Rome.
(It would be fun to see someone come up with a wacky POD that lets a Byzantine Emperor reconquer Rome and make it the Capital again to Legitimize himself)
Is it obvious? Where you see genius I see a reckless waste of resources on devastating campaigns which ruined Italy and cost the Empire dearly. Sure, it wasn't all bad, and taking North Africa, Sicily, etc. were good plays. But the Italian campaign was ruinous, and Spain just unnecessary.
Generally I see him as someone with that specific personality type to accomplish grand projects - an intelligent man to be sure, but also a bit paranoid and maybe a little megalomaniac.
One way or another, he'd find something to spend Imperial resources on. Given the Roman history of campaigns against Persia, I can see any invasion that way being every bit as much of a brutal grind as the invasion of the West, and potentially for even less gain.
I agree with Dorozhand that someone will try. In a timeline I wrote, it was the general Flavius Vitalianus, after a successful coup, to shore up legitimacy and otherwise for many of the same reasons as Justinian. Arab invasions are likely butterflied, as is Islam. Potential wildcards abound to break up a Roman-Persian stalemate - something has to give, regardless, I think.
Justinian did pretty well though. Maybe not as well as possible, but anything too much better and I'd probably say it was an Rome-wank.