I think a computer built like the Amiga would work incredibly well even today. I mean, there's a reason why consoles are so popular. People like custom hardware, and making a custom computer with the option of adding extra hardware could do incredibly fine.
And why would the custom chips be so incredibly outdated? I mean, the PS2 has custom chips developed by Sony, and that wasn't exactly outdated when the console was released. Even after all this time, some games look better than anything on the market. If you could get developers to develop for the custom chips, which I think they would do at least the first couple of years and then move forward to the extra hardware added to the computer.
I would ABSOLUTELY support such a project, especially if it would be an Amiga, and was backwards compatible. And I don't think adding the AGA chipsets would work fine, like how the PS2 have a PSone included. And no, the PS2 doesn't EMULATE a PSone if anyone wondered.