I actually went through this last week. The problem is that, if the power goes out (presumably without advance warning), a bunch of triage to basically turn your freezer into a cooler for critical items is going to cost a bunch of the stored cold air.
I'd probably go instead, if you have a cooler, with buying a few bags of ice if you can and quickly pulling out high value/especially perishable items and putting them in the cooler.
You don't have to be so quick about it. The heat capacity from warm air coming inside is dwarfed by that of the frozen solids and especially their latent heat absorbed during the melting process.
You're right. If things had gone on much longer, I'd probably at least have tossed a few bags of ice in my main freeze. (Probably better than pulling stuff out and so forth.)
I'd probably go instead, if you have a cooler, with buying a few bags of ice if you can and quickly pulling out high value/especially perishable items and putting them in the cooler.