It's been done before. Lots of 90s bootleg consoles used clones of the Famicom/NES chips, though they weren't particularly accurate clones. The Commodore 64 Direct-To-TV of all things had a custom ASIC made for it in 2004.
I think these days FPGAs have just gotten cheap enough that the economics of making custom chips doesn't make much sense for the volumes these kinds of products tend to sell.
I think these days FPGAs have just gotten cheap enough that the economics of making custom chips doesn't make much sense for the volumes these kinds of products tend to sell.