Why would he need to stick with it? Why would he use that model in a way that makes every single species look like it evolved through common descent? Is God intentionally deceiving people?
Yes, good point, the God portrayed in the bible would not go out of his way to make things look evolved.
There are some severe problems with homology as an argument for common ancestory. The most common one you will hear is that homologous structures often develop in totally different ways, so for instance, embryonic fingers can develop by a) growing a web and killing off the cells between the fingers (apoptosis) or b) budding, the fingers bud out from the hand. The finished structures look the same, but the path they took to get there is completely different.
You do realise that this argument requires hyper evolution at a rate never seen? Multiple species of big cat would need to have evolved in extremely short timespans (and they would need to do so without leaving evidence of the genetic bottleneck that results from starting from only 2 animals). Ancient Egyptian writings contain references to lions, leopards and cheetahs.
What do you mean never before seen?
Evolution in the fast lane | New Scientist April 2, 2011
Stickleback Evolution
The common experience for breeders is that you take an animal from a mongrel (mixed) gene pool, you can breed it up and evolve it very very quickly to get it where you want it to be, but then you hit a barrier, as it were, after which you get less and less return for the amount you breed it.
Focus 31(3) (see "Do greyhounds have a speed limit, about three quarters of the way down the page)
We see the same in weat. My molecular agriculture lectuerer said that we have had 40% increase in wheat yields in the last half century, but we are not really going to get very much more increase by further breeding.
Creationists do not recognise this as evidence for Darwinian evolution, because what has happened is that you have just selectively eliminated all the unwanted genes from the gene pool, then you can get a bit of extra evolution by mutations, but these are generally destructive mutations, and then you reach a point where you are only going to get further evolution if you have constructive mutations.
Darwinian evolution requires these constructive mutations, and creationists say that genuinely constructive mutations cannot occur by small micro steps.