A rugged spill-proof DJ-focused mini pc similar to Intel's recent NUCs in a dashboard form factor would be awesome but would probably be considerably more expensive than your estimates. (https://www.engadget.com/2018/04/10/intel-hades-canyon-nuc-review/)
With current laptop/desktop kind of power and IO, one could run a high-rez touch interface smoothly at 60fps, output HDMI video, add a built-in DMX socket for lighting and leave plenty of headroom for future growth. Other than a custom touch UI it could run Rekordbox DJ code as is. It could even power future DDJ controllers over a single USB-C, if they'd only implement it.
It'd be fantastic as a modular add on to DDJ controllers and an easy hub to squeeze into existing DVS and CDJ booths.
I don't think Pioneer would be so bold. I think IF they did this they'd go for older, cheap, reliable low power ARM/SOC processors and a custom OS similar to the XDJs. Unfortunately this would likely rule out HD video, complex FX , lighting and other high end features. Possibly even 4x track playback too. At which point the benefits over the XDJ range become difficult to justify.
Pioneer is not going to give anyone 4 channel standalone pro-level performance cheaply. Only if the competition really forces their hand. But with an ecosystem leaning hard on their installed base and established name they are very comfortable. Comfort doesn't typically foster innovation.
I don't know what processor Denon are using in their SC5000 but it's so far ahead it actually makes even Pioneer's top end gear look like old pocket calculators. Perhaps if the competition snaps Pioneer hardware R&D awake we could end up with an embedded processor fast enough for what you/we want. Even so, it'll take some time. Look at the pace of innovation in the CDJ line (CDJ-2000 circa 2009) vs mobile devices over the last 10 years.
Perhaps what we'll see is something like the Numark Dashboard. 3x 7" touchscreens screens, a few dials and buttons but the brains remain on a laptop somewhere off to the side. Less ideal, less ambitious but more likely.