If Apple 'thins out" out the low end Mini ( only a plain Mx (M2, then M3, etc) more plastic , less aluminum , smaller power supply , etc. ) then they probably can get the costs down.
At one point the base configuration of the Mini was $499. If Apple could squeeze a "smaller" Mini case with an M2 down to $599 then folks who want the "bigger home A/V unit" could be pointed to stretch to that price point and the Mini. When the Mini was around $499-599 it was used more as a "Home Theater PC" (HTPC). [ If they were looking specifically for the HTPC use case could chop the SSD back to 128GB. That is double the current ATV 4K max capacity of 64GB and there are USB/TB ports on it if will to stick on an external drive. Could also likely weave in the much of the kiosk and digital display use cases also with 128GB . ]
AppleTV is already relatively expensive. Calls for even more expensive bill of materials is highly likely going to end up with an AppleTV that is substantially more expensive. ( Apple is probably not going to take lower margins.).
If willing to pay more than $500 ... get a Mini. It has the Apple TV app. The Siri Remote primarily uses Bluetooth; the Mini has bluetooth ( old school Mini's had a IR receiver, but don't really need that these days. Between HDMI-CEC and bluetooth. )
The all-new Siri Remote that launched with the second-gen Apple TV 4K has been a hit. And with the refreshed...
9to5mac.com
A more expensive AppleTV device isn't going to help it with the major market forces it faces.
1. The AppleTV app is already on (or downloadable to) the "more than decent" TVs from the top 3-5 vendors. (at least in the USA).
Also on Playstation and XBox and the other streaming boxes ( XFinity , Roku , Andriod/Google TV , FireTV , etc.)
2. Most of the streaming competition is below $100 , let alone $300. Most of the primary market is price anchored to double digit price number.
For the gaming box segment Apple is just highly unlikely to follow the "Sell box at almost no margin and make it up on game licensing". Apple doesn't "loss leader" products are a basic practice. All the devices make their own money. The software products are gravy on top. By the time have thrown in the higher end bill of materials and toss on top Apple's desired margins... probably in the zone of what the low end point what the Mini used to be.