Don't want to be that guy, but as krick pointed not long ago; today you can have an i3-9100F at 90€, a monster for the price, with a 70€ micro-ATX mobo (even the H310C aka H310 R2.0 that support W7), and any of the AMD gpu's supported by CRT-Emudriver (even still several low profiles easily found if volume is a concern)
So I don't understand the persistance for AMD APUs considering the known poorer performance in MAME and - now further confirmed but we saw it coming - significant potential for issues and limitations.
I agree that this is not an obvious or smart choice for an emulation box. If the aim is to build a cheap and tiny mame-only box that outputs analog RGB at native res, that niche is already filled very well with the Raspberry Pi. If it doesn't have to be tiny, you can get a better used mini ITX setup for less as you said. If it doesn't need analog RGB, mame will run well on almost any decent smart phone these days.
I use my phone and tablet for mame when I travel (which is the only time I need my mame box to be tiny). Mame really doesn't need much horsepower to run well:
Mortal Kombat 3 on my phone:
SF2 CE, Ridge Racer 2 and Final Fight on my tablet:
I think most of us here would want the option to do more than just mame though. Most of the emulators of more up to date systems like Dreamcast / Naomi require a decent CPU and GPU to run well. If saving space is the goal, it's usually better to have one machine instead of two. I haven't managed this myself yet though.
Even though GM now works with some fairly powerful AMD GPUs, some of the newer PC based arcades in Teknoparrot seem to need an Nvidia GPU to run well. I've concluded that this hobby just doesn't lend it self to space-saving minimalism. We all need at least 2 PCs as a minimum. Unless you have s teeny tiny house, there no need to worry about space.