Could you not just run a 240 volt outlet on existing wiring built for 110v? Just send l1 and l2 on the existing hot/neutral?

You can, 240V on normal 12/2 Romex is fine. The neutral needs to be "re-labeled" with tape at all junctions to signify that it's hot, and then this practice is (generally) even code compliant.

However! This strategy only works if the outlet was the only one on the circuit, and _that_ isn't particularly common.

Although this exists, as a layperson, I've rarely seen it. There is the NEMA 6-15R receptacle type, but I have literally none of those in my entire house, and I've really never seen them. Apparently they're sometimes used for air conditioners. Aside from the very common 5-15R, I see 5-20R (especially in businesses/hospitals), and 14-30R/14-50R for ranges and dryers. (I have one for my range, but here in the midwest electric dryers and ranges aren't as common, so you don't always come across these here. We have LNG ran to most properties.) So basically, I just really don't see a whole lot of NEMA 6 receptacles. The NEMA 14 receptacles, though, require both hots and the neutral, so in a typical U.S. service panel it requires a special breaker and to take up two slots, so definitely not as simple of a retrofit.

(Another outlet type I've seen: I saw a NEMA 7 277V receptacle before. I think you get this from one phase of a 480V three-phase system, which I understand is ran to many businesses.)

If you drive an electric car in a rural area you might want to carry around 6-30 and 6-50 adapters because most farms have welders plugged into those and that can give you a quick charge. And also TT-30 and 14-50 adapters to plug in at campgrounds.

NEMA 6s are extremely common in barns and garages for welders. 6-50 is more common for bigger welders but I’ve also seen 6-20s on repurposed 12/2 Romex as the parent post was discussing used for cheap EV retrofits, compressors, and welders.

5-20R/6-20R is also somewhat commonly used by larger consumer UPS for your computer, router, etc.

NEMA 6 is limiting because there’s no neutral, so everything in the device has to run on 240V. Your oven and dryer want 120V to run lights and electronics, so they use a 14 (or 10 for older installs) which lets them get 120V between a hot and the neutral.

Oddly, 14-50 has become the most common receptacle for non-hardwired EV charging, which is rather wasteful since EV charging doesn’t need the neutral at all. 6-50 would make more sense there.

Reasons why it's nice to have a 14-50 plug in your garage rather than a 6-50:

1: when an uncle stops by for a visit with his RV he can plug in.

2: the other outlets in your garage are likely on a shared circuit. The 14-50 is dedicated, so with a 14-50 to 5-15 adapter you can more safely plug in a high wattage appliance, like a space heater.

1 is why we ended up with 14-50 as the standard, too. Before there was much charging infrastructure, RV parks were a good place to get a semi-fast charge, and that meant a charger with a 14-50 plug.

2 is something I never thought of, I’ll have to keep that in mind.