Maritime telescopes: Stabilisation requirements for optical vs. radio telescopes?
You asked for arguments against this, but I don't think there are any other than money.  Consider the AN/SPQ-11 passive radar that was aboard the US Navy ship Observation Island.  The actual receiver area is not as large (7M according to https://fas.org/irp/program/collect/cobra_judy.htm), but we could imagine a larger antenna being placed on a larger ship such as the USS Enterprise.  The beam (maximum width) of the Enterprise is 41 meters, which could certainly accommodate a 10-20m dish.
I think the only reason this would not be built would be lack of funds.  From an engineering perspective, it seems doable.