To be fair here, those who support the detention regime are also generally in favour of deportation. However, current US laws require amounts of due process (to evaluate the claim on its merits) that -- combined with current administrative resources -- result in a slow timeline for hearings and deportation.
Therefore, immigration advocates argue for continuing the past practice of release on bail-like conditions, whereas restrictionists argue that such release is itself a threat (e.g., claimants can 'disappear' as illegal immigrants) and detention is necessary notwithstanding the human cost.
In the meantime, there is also evidently an informal argument that detention itself should act as a deterrent, as weaponized cruelty. This argument is legally and morally reprehensible, but as far as I know policymakers have not officially made it.
People also want temporary residence to be given to asylum seekers, as specified in the UN Convention on Refugees. Allowing someone to remain in the country is not the same as granting them citizenship. It is also not the same as entitlement to benefits, entitlement to vote, etc.