A DSA is only going to be an order of magnitude or two more performant than a general computer on any given process node. They'll certainly slow down at the same time general purpose CPUs slow down. The thing is it makes more sense to design and include them in a world where transistors are potentially getting cheaper without getting better because a finite amount of engineering effort will be stretched across a longer timeframe.

Does that also imply a potential power savings of an order of magnitude or two? Because then it becomes a lot more obvious that the demand for them will be there in mobile phones and laptops at least.

Yes, it does. And that's a big part of the push for dedicated co-processors that we've seen in SoCs.