3DS emergency price drop was announced 2 weeks before and with an ambassador program. The thing is this is the first major revision for a Nintendo console that price goes down and not up and they will kill even more an already slow May with a 6 weeks gap.
You do have a point re: price. But it's not just a price drop: they have to market the revision, allow retailers enough time for pre-orders, and lots of other things that needs preparing. The longer they wait, the longer it's going to leak. Besides killing sales ahead of releases is inevitable.
But right now, I'm not expecting any announcement this week (which means an announcement this week is now 100% guaranteed).
It also worth noting, the 3DS XL reveal received a 21 min direct including games, and the New 3DS's direct segment was only 17 minutes including games. So this next direct is within the right time, both in time-frame and running-time , for a hardware announcement.
You can't compare a general Direct with a game-specific Direct, which is meant to provide in-depth look at a game.
We also have to consider how much functions they have to strip away for the Switch Mini. Anyone remember the Wii Mini? That thing had a lot of things scrapped from the original Wii and I believe didn't sell that well. Anyone who has numbers?
They're not going to strip anything significant, as it was mentioned before this revision is seemingly replacing the OG model (though nothing has been announced, so best to wait and see).
But using Wii Mini as comparison is rather awkward, the two models couldn't be any more different. Wii Mini was a super low-cost model catering to very late adopters, released way after the Wii had stopped selling significant numbers (it came after the Wii U), and with lots of stuff stripped to only keep the essential. Not to mention it wasn't release in Japan, and initially only launched in Canada for some reason.
The new Switch model is meant to maintain momentum of the console, by attracting a large amount of people that have been holding off buying one. Even if it's a "mini", it'll be still a full-fledged Switch with all the features of the original.
You'd better compare it to the 3DS XL or New 3DS in my opinion.