Constantine could have wiped away the façade of a republic, and gotten rid of the senate as an administrative body- but it was too useful. It gave him a pool of ready-made rich men and military leaders from which to pick his Provincial governors.
That was already well in decline by the time of Constantine. In truth, it had been in decline since Augustus (maybe even Marius), when the military reforms started to ensure that military leaders were no longer restricted to the senatorial class. The process had been sped up rapidly by the third-century crisis, and by the time of Diocletian and Constantine the Senate was already operating as something of a fifth wheel, and emperors were increasingly inclined to choose provincial governors and fill administrative offices with members of their own entourage.
But, that being said, I agree that it's probably too early to eliminate the Senate, even if it's no longer strictly relevant to the running of the empire. The tradition is too powerful, and it took another couple hundred years before the Romans/Byzantines truly dispensed with it in name. It's
more plausible that Constantine might have decided against creating a secondary Senate in Constantinople, mind you: previous emperors had established their own imperial capitals in various cities (Milan and Nicomedia, to name just two), without feeling the need to create new Senates. But Constantine wasn't just interested in creating a new administrative capital: he wanted his new city to have all the culture and prestige of Rome itself. And for that reason he needed a Senate: not because it was particularly important to the running of his empire, but because it was an issue of prestige.
However, ridding the Empire of the nominal existence of the Assemblies, from which he derived his legislative powers, would have never gone through. At least not at that time.
Agreed. It's a testament to the longevity of Roman cultural memory that they still clung to the concept of the assemblies, theoretically speaking, several hundred years after the assemblies had last actually assembled....