Are Chainless Belt Gears The Future of Bicycle Drivetrains?

Why too mechanically complex, plus chains are cheap and efficient and if encased, requires very little maintenance.

I wish encased chains were more of a thing outside of the netherlands. I would take an encased chain over a belt drive.
- You can buy chain cases on amazon, though it requires an internally geared hub.
Definitely.
I've ridden in some nasty conditions, and my chain didn't have that "filth" they showed. That's a result of using a lube that attracts and holds goo, and using too much of it. (It's been a while, but modern lubes which include things like waxes prevent this very problem).
I really can't see a way to beat the chain drives we have. For the same weight and space as this belt drive, you can have 20+ gear ratios with chain, and have it work near flawlessly 99% of the time.
I can already see a problem with this belt drive - that tooth arrangement with the bar in the middle will be problematic. Let just a teeny, tiny pebble (say 1/16" or 1-2mm) stick to that belt because it has a little water/mud/street grime built up and it'll jump. Or that goo getting onto that shifting mechanism... It'll grind and bind terribly. Funny how they compare their pristine mechanism to a "filthy" chain. This stuff operates in "filthy" environment - and this solution has far finer tolerances than chain drive.
Finer tolerances for better performance just mean a tighter perfomance window.
Edit: still ingenious engineering and very cool to watch
- Wet lubes are notorious for attracting grime. Lube up, let rest overnight, wipe off excess day after and that grime still builds up quickly. And since the grime is stuck in the lube just washing it off isn't enough. Requires a good cleaning and then new lube.
  Wax is a great option but all wax solutions I've encountered requires a very clean drivetrail. No oils, lubes, grease etc or the wax won't stick. More prep work but so worth it in the end.
  I would love to go belt drive and there are high end internal hubs that offers similar range to 12spd mtb gears. Tech is there, tech is working but cost is still too high for me. More likely I'll go belt drive when (if) I get me a touring/bike packing bike.
  That said this mechanical solution looks too engineered to get wide adaptation. 2-3spd gear hubs are tried and tested. That said again this combined with a moderatley priced 6-8spd hub could be cool. Cool in a frankenbike kind of way.
  Still. Cool tech demo/proof of concept.
Alternatively, I've found that having a long front fender (i.e. mud flap nearly to the ground) can reduce chain contamination by a significant amount. I rode all winter, and we salt/sand our roads, and I didn't have any issues with excess wear, rust, or anything like that.
Just wiped the chain with a microfiber cloth after my ride, and I was good to go. This was on cheap ass 8 speed chains, too!

Way too many moving parts for only two gears. Also, only two gears, so no.

I think it could be nice if it fits internally geared hubs, but otherwise it's only slightly better than fixed gear

Yes but not like that. I have 2 belt-drive bikes with internal hub gears. For a utilitarian city bike, I think there's nothing better and they will be much more common as more people try them.

List of benefits:

Basically no maintenance required. You might need a yearly oil change.
You can change gears while stopped
Nothing oily to get your pants dirty
Virtually silent. The ones I have don't even click while free-wheeling.

Downsides:

Most internal hub or gearbox transmissions don't like changing gears under load
They're heavier than a chain and derailer setup
They're generally more expensive
They require a frame that can split somewhere in the right side chain or seat stay. This isn't a problem if you get a bike with a belt but it makes it pretty much impossible to convert an existing bike
To change your transmission, you need a whole new wheel (or de-lace, and re-lace your existing wheel).
There are fewer options.
Generally, you have fewer gears

Also, internal hubs feek inefficient compared to external, worm gears.
I have rebuilt 3-speed ones like Sturmey Archer, despite being told by the bike shop manager I worked for that it was impossible.
Thete were 2-speed hubs that shifted with a brief backpedal, rode one for years, no external controls, just a slightly larger and heavier hub.
- Worm gears? Internal hubs are generally less efficient but that only really matters when you're racing. For groceries, the extra reliability is worth it to me.
Is it easy to repair a flat tire, on a belt bike?
By easy, I mean at home with basic tools, not at roadside on a rainy night.
That is my main worry about belt and internal gearbox bikes (I have flats quite often even with new tires)
- I'll let you be the judge. This is the official instructions video for my main bike.
Me riding an SLX drivetrain with an ebike-specific KMC chain without cleaning or lubricating it for 2 seasons: No maintenance required
Virtually silent. The ones I have don’t even click while free-wheeling.
I actually view this as a downside, or at best neutral. I find the click of free-wheeling to be the most effective way to alert pedestrians to your presence, because a bell should not be used except as an equivalent to a car horn (and pedestrians often react unpredictably if you misuse it), and your voice can sometimes come across as a little aggressive even if the intent was purely informational. But the click of a freehub makes it clear you're there, while also making it clear that you're slowing down and being patient/careful.

Belt drive with a gearbox is basically superior to chain and derailleur in every way but only on ebikes. I'd gladly take that on my bike. It takes about 2 weeks for me to bang my shifting out of whack after I've adjusted it. Though I've gotten pretty good at twisting it back into correct(ish) position trailside by my hands.

Belt drive with a gearbox is basically superior to chain and derailleur in every way
Unless you ignore cost, maintenance, dealer network/service centres, added weight, efficiency loss, special frames, worse gear ratios, and fewer upgrade paths.
But the advantages can often outweigh these negatives, depending on use and user.
- You may have meant ~~Unless~~ If you ignore cost,...
  If so, I heartily agree. That said, I'm contemplating a Rohloff ebike build... and would choose that for an around the world tourer...
- To my knowledge they only require an oil change every year or so and the belt doesn't require any maintenance. Chain and a derailleur need that constantly.

"Belts are clean, silent, and can last 3-4x longer than chains.

Sounds like waxing a regular chain will give you the same benefits, and you can continue to use readily available components at minimal cost.

That said, I'd get a belt drive on a bike meant for our crappy winter and salted roads. I can absolutely see the benefits with that.