As I understand it, the newly announced policy for detention of alien families, is intended to provide a place for these families to stay while awaiting adjudication of their immigration status.
What Acting Secretary McAleenan described as the facilities here obviously will be costly, a cost presumably borne by DHS. What McAleenan doesn't address are the costs (for example, per family per day).
The incarceration or detention of these families appears to be to insure their attendance at hearings or proceedings on their residency status. DHS has claimed that approximately 80% of those required to attend/participate in their adjudication do not appear, so the detention necessary.
The previous administration was faced with a similar problem (non-appearance) that they attempted to solve by Family Case Management used case workers in five U.S. cities to help migrants navigate the immigration court system. The program cost less than $10 a day and had a 99 percent success rate with court appearances and ICE check-ins. ICE cancelled this program claiming it was too costly.
Another alternative to detention of families (who importantly, had no criminal background) was the use of electronic ankle monitoring at $4.12 a day. The ankle monitor program is managed by GEO Care.see here
Without understanding the cost of the newly proposed facilities, it is impossible to understand if it is the most cost-effective way to insure compliance with appearance requirements.