After a little research, I learned that a feature of the counterflow assay is that the high internal concentration of the unlabeled substrate acts as a competitor to minimize the exit of the radiolabeled substrate once it has been taken up into the liposomes. Another way of stating it is that when the radiolabeled substrate enters the liposome, its specific radioactivity is greatly reduced by dilution with the unlabeled substrate, so that whatever substrate molecules exit the liposomes are most likely to be unlabeled ones.

The result appears to be that a larger amount of uptake can be achieved with the counterflow assay than with uptake into unloaded liposomes. I find this to be counterintuitive, because I would expect the concentration gradient (higher inside) to work against uptake of external substrate, but you can see the comparison in the paper linked below (Figure 1).

https://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC323357&blobtype=pdf

Here is another paper that gives perspective on the uses of the counterflow approach.

Article Biochemical Characterization of the C4-Dicarboxylate Transpo...

Here is an earlier paper using the technique.

Article Solubilization and reconstitution of the lactose transport s...

I think another advantage of the counterflow method is conservation of expensive radiolabeled substrate. Loading the liposomes with radiolabeled substrate is wasteful, since most of the substrate gets thrown away with the external medium. Diluting liposomes loaded with inexpensive unlabeled substrate into a medium to which radiolabeled substrate has been added probably uses a lot less of the radiolabeled substrate.