And you just proved my point, Caesar had more organized swords and more ruthlessness. At this point you do protest too much.
Caesar also got fucking assassinated because he couldn't convince people (including Brutus, one of his closest friends and lieutenants) he wasn't going to become a tyrant, despite being a vastly more palatable candidate for leadership to the Roman elite (an aristocrat from an ancient & storied patrician family, a highly experienced & popular war leader and statesman, and even a more merciful man in victory than many of his predecessors and rivals in the previous civil wars) than Arminius could ever have been. You can't hold power without political legitimacy and that stuff doesn't exactly grow out of the sword you used to take power in the first place, who knew?
Assuming they could all agree and not use this as a pretext to push their own agendas. Especially as Tiberius' early reign had several legions revolting.
You said it yourself earlier, even the Senate doesn't particularly want power back unless they have no other option due to bad memories of the late Republican years. Germanicus is the next most obvious heir to the Julio-Claudian dynasty after Tiberius, a proven leader, and hardly seems an offensive choice to them or the Praetorians if all the accolades about his virtuous character are even close to accurate, nor has he done anything in history that we can point to as a sign he'd anger either faction to the point of becoming his intractable opponents. Nobody in 14 AD could possibly foresee him dying in five years' time (if that even still happens ITL) without an actual gift of prophecy and with him assuming the purple, they can push any further jockeying for power behind the scenes once he's enthroned.
Germanicus also handled the 14 AD mutiny fairly smoothly and without having to engage in pitched battle or a massacre, so well in fact that the mutinous legionaries wanted to declare him emperor - and unlike with Tiberius, he certainly has no reason to say no if his nearest rival for the purple is Arminius. So I'd say that's yet another point in his favor.
If by kicking Arminius Ass you mean getting fought to a stalemate in one battle, failing to close a trap on Arminus in another and suffering unsustainable losses which even Tiberius had to point out to him as he ordered him out of Germania. Sure he got 2 legionary eagles back, but the amount invested did not gain the return expected and the Status Quo remained.
And again if Augustus is out of the blue choosing Arminius with no explanation over his own relatives, would the Senate and Legion Commanders even trust the Julio-Claudians further than they can throw them? They could ignore Caesar's dalliance with Cleopatra as he was never so foolish to marry her or make Caesarion heir. But Augustus declaring a barbarian an heir, at this point they are probably thinking something is wrong with the bloodline, time to find others or once again go back to Senate Rule but try to make it work this time as it did in the old days.
And it is not like there is a shortage of other prestigious families with a good head on their shoulders that can use this to their advantage to rise to power.
Germanicus also mauled Arminius' forces, captured his family and prevented him from ever putting together a coherent, permanent anti-Roman coalition among the Germanic tribes. (Hell, not only was Arminius himself eventually killed by his fellow Teutons historically, but the Romans would eventually put his honestly pro-Roman cousin Italicus on the throne of their tribe) I'd rate that a solid ass-kicking success overall even if he couldn't literally parade Arminius himself in chains in a triumph back at Rome, especially since the Germanic peoples no longer posed a serious threat again until the Batavian revolt many decades afterward.
The Julio-Claudians survived the much more obviously & consistently nutty Caligula not even a full three decades down the road and even in far later, far harder times the Severans survived the downright psychopathic Caracalla. As severe a lapse in judgment as Augustus' last act in this life might be, it's not necessarily an insurmountable obstacle that is certain to destroy the dynasty, especially not given Germanicus' credentials and excellent reputation.