I think it's difficult to envisage a "market" for custom consoles with specific features, akin to the Mini Consoles as you say, because there are so many potentially customisable variants that it's unlikely your product offering would meet the exact desired specification of a buyer. For example:
Banjo wrote:3. Previous gen consoles with the complete suite of releases from a given publishing house (A Capcom Xbox 360 for example).
Let's say someone does look to produce a Capcom Xbox 360 ie a console which contains a digital version of every Capcom release on its hard drive. To create this would take a console generation's length of work (and investment!), possibly several times over if they want to sell multiple consoles. So it's a very costly product to create in the first instance. And what if the buyer is wanting specific DLC, or certain games not available to the PAL market, or a specific themed console e.g. maybe they want all this on a Street Fighter 360 to complement the Capcom theme?
Add to that the fact that digital downloads can often be tied to the purchasing account, meaning your prospective buyer of this custom console would only be able to play on it as the prior user. While retro buyers know they're not buying new, they like to simulate that new experience. What's the first thing most people do when playing a "new" game for the first time on a second hand game cart? Erase the former owner's save data and start afresh. I can't see people paying premium to inherit several years' worth of someone else's save data, achievements and all. And I'm not sure many buyers would sell on a console still linked to their account if said account still knows all their payment details - but if unlinking the account removes access to the software, it is no longer a viable sale.
It would be interesting to know if anyone out there on the world wide web is curating a list of "unplayable" classic games. Unlike most other media, gaming is unique in its lack of a universal format, and its switching of formats every few years, meaning it's more possible for classic releases to be lost forever. Great albums are always re-released, great movies likewise, but not all great games. I've mentioned Goemon on the N64 more times than is fashionable, but as no official Memory Cards still work without modification and battery replacement, no unofficial Memory Cards work at all, and the game requires a Memory Card to save progress, it isn't possible to play the game properly for more than a few hours before having to start all over again when you resume your session. To me that's a "lost" game - one that's impossible to properly play as the developers intended in 2020. There are many, many others, such as the delisted games Cora mentions.
The other problem with a lack of a universal format is that it makes it difficult for companies to re-release these classic games. Bigger hardware manufacturers like Nintendo and Sony have the luxury of being able to decide their approach and create mini consoles or services through which classic games are played, and they may choose to involve other developers in that model - so there are a few that benefit through inclusion e.g. by their games being included on the SNES game selection on the Switch, or on the NES Mini. But that means the console span is limited by the publisher - so even if Konami get picked and NES Track and Field or Metal Gear sees the light of day, it still doesn't give them an option to republish MNSG, should they want to. Their options are then digital - where the market is already crowded, and multiple fees are to be paid to the digital market owners, be that Steam, eShop, etc - or remake / remaster, which isn't financially viable for most games.
The longer we go on for, the more sizeable the "retro" market becomes as more games become suitably old. I think until there is another major shift in the gaming landscape, the pre-digital cutoff will remain the point at which most games are considered retro - any game or system that requires you to register an account using an email address you still use will be hard to consider as retro in the same way as a game you used to have to dust before putting into the console to make sure it would work! There does seem to be a bit of a "squeeze" happening with retro gaming, in that the really old stuff is being re-released and the newer stuff not yet old enough, so it's those middle releases - that N64 / PS2 / turn of the millennium era, and particularly handhelds - that aren't getting much attention save for some high profile remasters, and are thus more likely to attract high pricepoints for prospective collectors.
It seems bizarre to me that Nintendo, a company well known for disliking anyone else profiting from their intellectual property, would be so happy to allow a burgeoning retro scene to develop (as Nintendo stuff seems to hold its value very well - but that's always resale value, of which Nintendo sees £0) so I'd expect them to be rereleasing old games left, right and centre. But perhaps they're more savvy than we give credit for, and maybe they (and other developers / publishers) are happy to allow the scene to develop on its own, knowing they are fuelling a demand for the unattainable and stoking interest in a group of consumers that will ultimately benefit them. It's hard to see a generation of Instagram collectors and cosplayers posing with digital downloads, for example - yet that's ultimately the content that creates the newer generation of buyers for new game releases from those same companies. The problem is that this means great games by companies who've failed to maintain their position will inevitably be consigned to history, their memory kept alive only by a select few posting on games forums about how a blue-haired satire of a medieval folk hero once saved imperial Japan from aliens wanting to conquer the world and turn it into a stage production.