There's roughly two factors playing there.

First, a matter of political and cultural identity : the distinction between a Barbarian and a Roman in the Vth wasn't necessarily cultural (Barbarians being increasingly "Romanized", not unlike Later Jin were in Chinese history, while preserving a political and identity distinctiveness) but both political and genealogical.

Technically, a Barbarian was whoever followed and obeyed a Barbarian petty-king : they were part of a people federated with Romans, but not Romans themselves.Whoever else that ultimately obeyed or served the Roman state was a Roman, even if they had Barbarian origins.But Romans weren't "Genealogy-blind", so to speak, and Roman citizens whom relative were Barbarians (critically if these relatives were leading Barbarian peoples) were often considered as semi-Barbarians at best.It's why people as Stilico or Ricimer, in spite of being generalissimos and de facto co-emperors in their times never were in position to hold the purple (although Stilico might have attempted to do that for his children, there's no real sign Ricimer really tried to pull something like this.

In the case of Odoacer, it's even more clear, as he was proclaimed king of several federated peoples. Regardless of his romanity and his military service to the Roman state in the 450's-460's, one couldn't be Barbarian and Roman Emperor.

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Another factor was that the Empire well survived in the Eastern provinces : the emperor in Constantinople was still powerful and had a de-facto seniority in legitimacy : several late emperors were never considered such by them including Romulus Augustulus. Constantinople supported Julius Nepos' claims to the imperium in 476 while he only controlled Dalmatia (whom he personally inherited leadership).

Odoacer, like all other Barbarian and Roman warlords of the Vth century that cut for themselves a part of western Romania, needed some legitimacy especially as senatorial elites in Italy still well survived the general political collapse. Not able to be emperor himself, and unwilling to replace an illegitimate emperor by a new one (especially as Orestus himself was at least Roman, and that Ricimer's emperors were at least placed with assent of Italo-Roman elites rather than just put on the throne out of the blue), Odoacer wanted to appear as a vice-roy of sort for the legal imperial authority.He then send the imperial insignias to Constantinople, acknowledged a formal allegiance to Constantinople and to Julius Nepos (that remained stuck in Dalmatia) doing so.

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Late western Empire was falling prey to warlordism, mostly Barbarian (Euric, Gondioc, Clovis, etc.) but Roman as well (Marcellinus, Syagrius, Ricimer, etc.) that took over structures of the collapsing empire.But while stabilizing and legitimizing their rule they had to rely on at least formal imperial acknowledgement and legalism either having to build a compromise with the regional Roman elites, either due to the inherited "ideology of power", trough a state-building evolution in the Vth to VIth centuries. And this evolution wasn't just a matter of inner perspective, but as well outer as the Eastern Roman Empire remained a very powerful polity able to intervene in Italy and Africa directly, and sending subsides and prestigious goods to Barbarian kings acknowledging this relation.

Sources

- Late Roman Warlords, Penny McGeorge

- Fall of Rome, Peter Heather

- Warfare and Society in the Barbarian West, Guy Halsall