I'm not so convinced they did this slyly - I still think when numbers start to grow quickly you have no choice. HOWEVER, if they did, they are in big danger of being hoist by their own petard.
They are next scheduled to play on 3rd Jan - 6 days away. They have already declared they have 5 covid-infected players, who will now need to quarantine for 12 - 14 days. If they have used the numbers game for postponing today's game, they cannot possibly declare themselves able to play on the 3rd. And even then there's a good chance the numbers may increase.
So this could (should) put City out of action for 2 weeks at least, in a season that started late (so we're playing catch up anyway), in which they are still in all competitions, and where this deferment will give them the mother of all fixture congestions somewhere down the line.
On a practical level, I'd take our chances of playing them on their 6th game in 10 days when our best are hopefully back and we may even be able to have the benefit of a significantly larger home crowd.