I think there are two or three reasons Odoacer became the rex, or King of Italy, instead of the emperor of the Western Roman Empire. Firstly, he may not have been able to even if he wished, because he was a non-Roman barbarian. His father was a Hun, and his mother may have been a Scirian. Odoacer himself is variously referred to as a Scirian, a Rugian, and a Goth. Whatever his heritage, he was definitely not considered by the Romans to be a Roman. Therefore, he was probably affected by a de facto and unofficial prohibition on non-Romans becoming emperors. The direct evidence for this ban, however, is slim. While we have multiple extensive law books from the Late Imperial period, none contain any sort of reference to non-Romans becoming emperors. The only literary evidence comes from Philostorgius, who says that after the death of Valentinian II in 392, the high-ranking general Arbogast was unable to make himself emperor because of his non-Roman parentage. We know that Arbogast was a Frank. However, Philostorgius was writing from the eastern half of the Empire, and his work only survives in a ninth-century epitome, so does not provide anything close to an eye-witness account. Therefore it is not necessarily conclusive on its own, but circumstantial evidence can help make us more certain of this prohibition. In the fifth century, there were many powerful generals that controlled the Empire's armies. Of these, it was only the Roman generals Constantius III and Avitus who became emperors themselves. The equally powerful non-Roman general Ricimer instead cycled through multiple emperors that he controlled behind the scenes. This, combined with the evidence of Philostorgius, makes me fairly confident that Odoacer would never have been accepted as emperor by the wider Roman population, and the option of becoming emperor was unavailable to him.

However, it is also possible that Odoacer did not even desire to become emperor. Over the last century, the office of emperor had declined in power and prestige and had become a mostly ceremonial, figurehead-like position. Since the general Merobaudes had appointed the four-year old Valentinian II as emperor in 375, the western emperors had not held the real command of the armies and had been mostly overshadowed by their powerful generals. The last campaign across the frontiers by a western emperor was by Gratian in 378. Since then, the emperors mostly remained in the capital city, first Milan and then Ravenna, where they could be easily defended against invaders. Their power had shifted mostly into the religious world, and piety became a highly valued trait. I was shocked at the differences with earlier emperors when I first read that the Milanese bishop Ambrose publically claimed that it was emperor Valentinian II's child-like meekness that would endear the Empire to God and save it from invaders. A stark difference when compared to the ubermensch militarism of early emperors. Odoacer could have possibly changed the perception of the office if he took it up and remained a military leader, but the passivity of the office had become entrenched after a century of weak emperors, and Odoacer would have been pushing two boulders up-hill if he was also discriminated against because of his non-Roman heritage.

The final part of your question is why he did not follow the pattern of other non-Roman generals who installed figurehead emperors which they could control. Perhaps he felt Ricimer's manner of cycling through multiple emperors was too uncomfortable, chaotic, and risky. Another possible explanation comes from the embassy he sent to the eastern emperor Zeno shortly after over-throwing Augustulus. He told Zeno that one emperor was sufficient to rule the Empire, and he only asked for the title of patrician and to be allowed to control Italy. Perhaps there is some truth to this, as the western Empire was greatly diminished and hardly require an emperor to oversee it. You mention how Odoacer had control of the Senate in Rome, which is correct. These emissaries told Zeno that the Senate had accepted Odoacer as a competent ruler and they also asked for him to be granted the position of patrician, probably at Odoacer's insistence. Furthermore, if he or someone he controlled laid claim to all of the western Empire's territories, Odoacer may have been pressured into attempts to reconquer and regain control of the lost provinces. By instead becoming the rex of Italy, he only had to defend the peninsula, something he was much more capable of doing with the severely weakened army available to him. Finally, overthrowing the incumbent emperor and declaring himself or a puppet as emperor while Nepos was still in Dalamtia would have inevitably led to civil war, as it had for Arbogast in the 390s. Odoacer probably hoped to avoid such a confrontation, at the eastern armies had defeated Arbogast, executed his puppet emperor, and forced the general to commit suicide.

Thus, in summation, I think the most important factor is that Odoacer was under the pressure of a de facto ban on non-Romans becoming emperor. Even though he had control of the armies, and if he declared himself emperor there was little anyone could do to stop him, there were multiple other reasons why he did not want to be emperor himself, most prominently because of the current weakness in the office. There were also other reasons why he chose to become a patrician and rex rather than install a puppet emperor. Please let me know if you have any follow up questions.