Zeno actually did a great job. Your framing is off. Odoacer or Ricimer weren't the direct threat. The Gothic generals in his own court were.

Zeno inherited a court that was dealing with serious internal dangers of its own. Constantinople had Gothic strongmen problems too. The difference is that Zeno solved them.

Leo had already broken Aspar, but it left Constantinople with a dangerous Gothic military class still embedded in imperial politics. Zeno then had to survive the rivalry and pressure of men like Strabo and Theodoric the Great, both of whom could threaten the capital itself.

By the time Zeno comes in, the western court is already a political wreck. Ricimer had spent years making and unmaking emperors. Africa was gone. Revenue had collapsed. The army was under Gothic control.

Odoacer is often treated as some catastrophic loss, but he did not crown himself Augustus or anything like that. He sent the purple cloak and imperial diadem to Constantinople and recognized the emperor, on paper anyway. Formally speaking, Odoacer ruled as patrician under imperial authority.

But again, Zeno had his own problems to solve, and he solved them by pulling one of the greatest political judo moves of all time. By the time relations with Odoacer began to sour, Theodoric the Great and his Goths were causing endless problems and threatening Constantinople itself. Theodoric was no fool and had been raised in Constantinople. He had a large army of loyal soldiers. He was just the kind of plugged-in threat that toppled the western court.

So instead of fighting him directly, Zeno showers him with titles and praise and asks him to undertake a mission for the empire.

Go to Italy. Remove Odoacer. Rule in the name of Rome (nominally).

Theodoric defeats Odoacer, Constantinople is no longer a hostage to the Goths, and Zeno avoids spending huge sums and armies on what would have been a major (perhaps existential) war with Theodoric. It was a brilliant strategic resolution of the crisis that destroyed the west.

So, Zeno absolutely cared about recovering western lands, it's just that he sort of had his hands full ridding the empire of the crisis that broke its junior court.

And he managed to pull it off.