Old fashioned spark discharge starters run incredibly high peak current at a low duty cycle. Efficiency isn't a big problem. It's enough to keep the spark gap ionized, not to deliver real welding heat.
It's also not very reasonable to make, say, a double-tuned air core transformer (that, on account of its tuning, would achieve good efficiency: but the tuning is constantly changing with cable position and arc gap ionization), nor a well coupled, cored type (which would be absolutely monstrous to avoid saturation*).
*On the upside, it only needs to be unsaturated while the arc is weak, or completely absent: a few amperes, or nothing at all. If the current is high (10s of amperes?), the arc must be conducting, and HF start isn't much needed!
Regarding welding technology: I have all the stuff to design and build hardware here, but what's the point? I can't make anything under about a buck per watt. Maybe a third of that once it's into mass production in China, that's it. Or to put it another way: if you have a few dozen kilobucks floating around for a new product, and you have the connections for cheap production, I can be of help.
![Wink ;)](https://www.eevblog.com/forum/Smileys/default/wink.gif)
Tim