To be fair, Radix, I don't think the main objection is that God couldn't design an old-seeming universe, but that he wouldn't, at least not one that would show some sign of its true age. To create a universe with an illusion of age and no way to pierce the illusion seems a lot like an act of deceit, does it not? For example, we sometimes see the light of a star going nova or supernova more than 10,000 light-years away; if the universe was simply created with an appearance of age, then that star never existed, let alone exploded!
This winds up being the cosmological equivalent of claiming that dinosaur bones were planted by the Devil to deceive us or by God to test us, but that such creatures never walked. One could just as easily claim that the entire universe was created five minutes ago with an appearance of age to the same effect.
That's why most Young Earth Creationists today spend time studying theories to show how the universe came to appear to be old despite being young. Speed-of-light decay (or CDK) is among the most popular of these (and I believe that a couple of Austrailian scientists proved at least some CDK in the universe a year or so ago, unless their experiments have since been falsified), but I personally rather prefer Russel Humphrey's alternative theory of the universe's evolution expressed in Starlight and Time.
To sum up: Saying God simply made the universe appear old, made it look like stars were being formed and were dying millions of light-years away (and millions of years ago) without positing a reasonable mechanic that caused the apparent age that we can test is saying that God purposefully deceived us. We only do ourselves damage by arguing this.
Personally, I take the I.D. approach and grant the evolutionist five hundred million years for life to form and evolve to its current diversity (though theologicially, I prefer a younger earth for simplicity's sake, I don't require it for Biblical inerrancy's sake). It still doesn't work, which is why so many scientists are either starting to make room for I.D. in their dogma or are positing ideas along the lines of panspermia, the theory that live evolved elsewhere before coming here (which is ludicrous and hardly to be preferred over the theory that God did it on purely scientific grounds, but there you have it).
How does this differ from Last Thursdayism? How do you decide which is correct?