This bike rack is at K&D. I can only lock the front wheel in this kind of rack, because the mudguard (or the derailleur on my other bike) won’t fit between the rack bars.
Fortunately the bloke who turned up and parked his bike as I was unlocking has the solution:
Park the back wheel next to the rack bars, then put your lock through the back wheel and the rack bars. Done!
So what’s to stop your front wheel going to a new home? The first pic seemed to show the bike secured through the frame; it’s a lot harder to walk away with the back wheel instead of the front. For a reasonable quick stop in a very public place, I think I’d go with the first pic.
Good point about a front wheel being easier to remove than a back wheel. I often have panniers on though – then I want to lock up through back wheel, frame, panniers.