How useful was Aetius as a hostage to Alaric? Did Honorius or Stilicho care that Alaric had taken him? Why did Alaric need to give up the hostage to the Huns and why did they look after the Roman boy? Could this have caused resentment towards the Visigoths when Aetius went to war with them after becoming Emperor?
Being an hostage at a Barbarian court wasn't necessarily being prisoner or a guarantee, but being a connection between Roman nobility and the Empire and Barbarian generals allowing them to be further integrated within the political frames of the Late Empire, notably by the establishment of friendly or even familial ties, or simply making their hostages more sympathetic to their own interests and perspective.
Thus, hostages as Aetius were fairly treated and associated with tasks or further education befalling to Roman nobility, the military and civil service; pretty much in the same way young Barbarian nobles could be held hostage among Romans, which was a long established practice and display of political power carried on by Barbarian generals.
When Alaric received Aetius as an hostage, the latter was barely in his mid-teens but already groomed into imperial service and issued from an important family : the Gothic general was negotiating from a not-too-strong position with the imperial court led by Stilicho , who previously defeated Alaric in 402 but tried to obtain the alliance of Alaric against Constantinople or other Barbarians.
After Stilicho's murder and the victory an anti-Barbarian in Ravenna, Alaric had still to negotiate with them to preserve what he gained so far without resorting to conflict. Thus, while Alaric could technically have refused to send Aetius away, doing so would have been too much of an hostile act against Ravenna, but as well Aetius' family.
Hunnic kings entered in a rear-alliance with Roman courts of Rome and Constantinople since their establishment in the Pontic region, then the Pannonian plain in the early 400's, and hosting Aetius certainly favored them in the aforementioned perspective : and indeed, Aetius became familiar with Huns and later reinforced the Roman alliance with them by recruiting them against Barbarians to a brand new scale, giving Huns more Roman subsides, more prestige against other Barbarians, etc.
- Generalissimos of the Western Roman Empire; John Michael O'Flynn; 1983