The thing about corn is they will eat it even when full. When the birds are about to coop up at night if you throw some down they will gobble it up. That extra quicker energy intake is not a bad thing. The idea is you are not replacing their total diet feed with it- not feeding it during the day. Fat is great for cold, fast to burn high energy. Is it needed? Not in most cases. What people deem cold and constantly exaggerate with wind chill factors are typically not the kind of cold where supplementing fat if warranted. I'll toss black oil sunflower down on mornings below 0 F. And when it's -10 F I'll toss it in the coop as the birds usually wait for temps to warm up later in the morning to come out and feed.
We eat BLT's almost every weekend here. The fat in the pan is absorbed into oats then fed to the birds. There is no concern of elevated salt. This salt concern is another perpetuated myth. What people need to remember is the salt studies were intended to be lethal. The birds literally had to be force fed salt (sodium solution injected into crops) as they would not consume it at those insane levels. Chickens are no more sensitive to salt than any other animal. We all die if force fed incredible amounts of it. The studies made sense to a point as in effects of salt, benefits at specific dosage. All animals need salt. Where it went off the rail was finding the lethal intake requirement. But you'll see all feeds have 1% sodium and that's the result of these often misconstrued studies.