I'm confused -- the H1 has no lens shift at all, and very limited zoom range. I hope you aren't recommending it to people that want a real home theater projector.
LED is dead for anything other than pico and entry-level projectors. The largest OEM's are moving to laser as they can get significantly brighter.
First, yes you are correct about the lens shift, my bad - they call it "wide-range keystone correction" on the XGIMI H1. The traditional approach for a nice variable optical lens shift feature is to physically move the entire lens assembly (either manually or motorized), which this unit does not do. Their approach, at least on my XGIMI wall mount, is (1) to use a bowl mount, which lets you angle the projector, and (2) use "extreme" keystone correction, which is a similar idea to lens shift, but is not real lens shift, so you are right. However, it acts similar to a manually-adjusted lens shift system, except you adjust the entire projector itself - adjust the bowl mount first to move the image up, down, left, or right & then adjust the keystone. Method is different, results are the same, although the primary benefit I've seen in the XGIMI's favor is there is no perceivable bowing visible (at least, not that I can tell). For reference, the original H1 I used had a vertical keystone of +/- 35 degrees & a horizontal keystone of +/- 30 degrees; the new H1S-Aurora does 45 degrees on both axis.
Separate from the lens-shift discussion, the wide-range keystone correction is absolutely phenomenal...you can place the H1 on the far left or right in the room, use the wide-range keystone feature, and get a perfectly square image in seconds. Very nice, especially for living room setups where you don't want a projector hanging from the ceiling in the middle of the room! The latest H1 models (ex. the 1200-lumen Aurora) also has integrated auto-focus, which works really well (mine has electronic autofocus, which is still good, but the autofocus is really slick!).
The zoom is only 1.1x optical, which isn't as much as say an Epson with a 2.1x zoom, and you have to use a little key to manually adjust it. Although you can also do Stepless Zooming, digitally (the newer firmware calls it Infinite Zooming, I believe - basically just shrinks the overall image without loss of quality). The combination of those is better than no zoom at all, which is the case for most LED projectors.
As far as 'real' home theater projectors go, it depends on what your definition of that is, which is really a matter of personal requirements, because the technology changes on a regular basis. I am pretty happy with my BenQ HT2050, but I would take an XGIMI H1S-Aurora over it in a heartbeat. It beats out most of the projectors I've installed in the last five or six years, for sure. I like it a lot better than some of the $5k-$6k projectors I've installed, tbh. And of course, if you're serious about your HT install, most people spend a lot of time geeking around over on AVS Forum in the sub-forum for their pricerange & do a lot of research selecting the exact model they want. Personally, having installed a ton of projectors over the years, I would absolutely call this a real home theater projector, without hesitation. I suppose the H1 could be considered an entry-level projector, based on the price range compared to the various models discussed at places like AVS Forum, but the PQ is outstanding & beats out a lot of other projectors I've both seen & installed. But then again, I typically don't do installs where the PJ itself costs more than $6k, so that's my working frame of reference.
I am currently not a fan of laser projectors (which is an opinion subject to change with the current crop of lasers coming out). I've installed both laser-only projectors & laser-LED hybrid projectors. I think they both look like crap. Good-quality LED-only projectors are better, but most run too cool (in terms of color temperature) even with tweaking. However, I am very curious to see how the new 4K laser projectors look. It looks like they've figured out the contrast issues that the early laser models had. I'd especially like to get some eyes-on time with Sony's 4K UST laser & with stuff like Optoma's "budget" 4K UHZ65 set, among others. Based on the CES footage, it looks like they have things figured out; the next trick will be getting it into a more affordable range. Nearly all of the consumer-level projectors I install for friends & family are in the sub-$1,500 range; I'd be curious to test something like LG's 1080p HF80JA.
Anyway, I am a big fan of the XGIMI H1. With how many vendors have skipped over LED, I'd suspect you're right in that everyone is moving over to lasers. I'm very interested to see what comes out in the laser arena over the next few years. For right now, today, though, I would go with an H1, unless you have a larger budget and/or particularly want native 4K resolution (especially with HDR, real lens shift, etc.). On a tangent, there's some really amazing ALR stuff coming out, especially from Screen Innovations...again, if they can get the price down (and I'm not just talking about the ALR-esqe grey Elite Screens & stuff), I think that a 4K HDR laser projector with a true ALR screen would be an amazingly compelling investment for people who want a big-screen they could use during the daytime.