With some exceptions, SEGA would prefer to pretend the Saturn did not happen.
This doesn't seem true at all. It was still their best-performing console in Japan, the market they sacrificed the West for that very generation. Hell, they saw fit to release MegaCD and 32X add-on props for the MegaDrive Mini in Japan when that was the MegaDrive's smallest market out of the Big 3.
If they're willing to do that for Mega CD and 32X, there's not much reason for them to run from their Saturn legacy. Besides, it's seemingly gotten a lot more popular in internet circles and the retro gaming community the past decade; global sentiment towards it isn't the same was it was in the '90s.
I think you need to consider what went into a Neo Geo Mini vs what would go into a quality "Saturn Mini" console before making the comparison. I'm far from an expert on this stuff, but the Neo Geo games have seemingly been ported/emulated extensively compared to Saturn games over the years. That could make the upfront cost of developing a little Neo Geo console significantly less than a Saturn console.
I could be totally wrong here, I'm somewhat apathetic about all of it because I still have a working Saturn hooked up to a CRT, but I just don't see a reason to put out a Saturn mini given the lack of interest in the mainstream audience. Most of the time when people see I have a Saturn, they think it's a weird thing vs. having my PS1 or N64.
That's the thing about anecdotal evidence; you can't fully use that as a widespread case. Like Saturn, Neo Geo also had a niche appeal (actually, a much narrower niche appeal), but again, that hasn't stopped SNK from releasing the Neo Geo Mini. Even if those Neo Geo ports are relatively easy to do, things from the costs of IC securement, motherboard design/prototyping/testing/manufacture, casing design, marketing, distribution etc....that stuff adds up. It's "cheap" compared to what Sony and Microsoft are going to be doing next year with their new systems, but it's not cheap.
They wouldn't need to aim the Saturn mini at the mainstream market. IMHO I don't see why they can't aim a bit upwards price-wise but make sure there's features present to make it worth it. Like the online connectivity that new Capcom plug 'n play seems to have (at least for firmware updates). Also I think a Saturn mini would actually generate
more interest than a MegaDrive one, simply because unlike MegaDrive, SEGA hasn't exhausted Saturn through minis going back over a decade. Never mind that Japan in particular would be a pretty strong market for it.
That's the way I see it, anyway.