As ever: "yes, but it would be a lot of hard work". If Apple wanted to, they could do it. I doubt it will be reasonable for the hobbyist community to do this. At least not without lots of existing experience, tools, and time.
I think new-build PPC Macs would be super neat and could avoid some of the physical problems existing PPC Macs have. A new G3 platform with a Rage128 or Radeon 7000 onboard, SATA, USB/FW, etc etc etc would be great, but I don't think it'll happen.
I also don't think it's practical to do and I don't think we have anybody with the skills/time/tools right now who really wants this.
Part of what makes "new" Amigas work is that the Amiga community rallies around the point of just... not actually caring too much about what really constitutes an Amiga.
There are, as noted, modern POWER and PowerPC computers you could buy. Most of them cost a lot and perform poorly, or cost a lot and perform well, but don't run "common" software. The modern "PowerPC" stuff is all going into either settop boxes or networking gear, which is why at least one of the Amigas has like... six SFP ports on it, even though that's not really a reasonable load-out for a desktop computer.
To be honest at this point my take is that emulation is basically fast enough that if you can't get vintage hardware or you have hardware with some kind of problems, using, say, QEMU-PPC is good enough for OS 9 and early OS X exploration. If you want to run OSX-PPC software (in particular) you can run 10.6 on Apple Intel hardware or hackintosh it, then install Rosetta. Even a middling mid-late Core2 era machine should run most PPC software under 10.4/5/6 very well.
W/re QEMU-PPC performance: I have run it on an i5-2300 and an i5-4570 and it's about as fast as a 300MHz G3, which is great for OS 9 but it falls over a little bit for 10.4 - it's fine for utility work but you wouldn't want to, like, make a
Gaming is a little bit out, it'd be bad on OS 9, sound doesn't work, so, it sort of depends on what you want to do. A QEMU OS9 instance would be great for compute, rendering, doing things that don't need sound, general productivity, touring the OS and old software, but maybe not great if your main goal is gaming or multimedia.
Refactoring an existing mac as jt suggests is also possible but whatever you refactor will still have the capabilities, limitations, and potential problems of the platform it came from.