I've read this analogy before, but it's weak enough to be inapplicable.
With wireless networking and even phones, the wires have actually been eliminated, replaced wholesale by something else, radio. A better analogy would be something like the powerline ethernet systems, but nobody is calling them something controversial like "wireless" or "cableless".
Put another way, I've seen cloud computing (of which "serverless" is, arguably, merely an evolution into increasing levels of abstraction) called "somebody else's servers". The equivalent with the Wifi analogy would be "somebody else's wires", and, usually, what wires there are, for the backhaul [1], aren't even somebody else's.
EDIT:
Ultimately, my point is this:
The analogy is weak becasue WiFi is not an abstraction layer on top of wired networking that merely hides the existence of (and, ideally, some of the downsides of dealing with) the wires, instead being a different technology with different upsides and downsides. Serverless is such an abstraction layer.
[1] Which brings up a nitpick: Wifi can remain even wireless in its entirety, with various mesh networking techniques.