That wait time, unfortunately, is long on human timescales. Also, there's the chance your ping was lost, so your phone tries at least a few times before giving up.
(I agree you make it seem pretty clear though, either it is silly or there are more details to be learned...)
This Quora thread is a good example of the typical non-answers provided to this question.
https://www.quora.com/Why-does-it-take-so-long-to-establish-...
Add more antennas, and you can say more things on more channels at once. "Enterprise-grade" multi-antenna routers (e.g. routers in conference halls) negotiate new connections much more quickly.
Cell towers are essentially a whole bunch of antennas (or a few antennae in highly-MIMO setups, so effectively the same thing) so there's comparatively next to no latency for sending "unexpected" packets to the tower.
(Establishing connectivity with a new cell is still hard, though, since it takes a moment for a handset to get the tower's attention when the handset doesn't yet know where precisely the tower is for MIMO-beamforming to kick in. This is ameliorated by many cellular ISPs mirroring connection state between neighbouring cells, so that when you move from one cell to another, the new tower is already "expecting" you.)
Since connectivity takes (far) less than 10s on enterprise-grade multi-antenna routers, all that time is being spent in some component that's different between the two classes of hardware. So looking at the difference in BOM between average products of the two classes might be helpful in figuring things out.
Otherwise, I hope things have been going well, btw =).
My naive intuition would just say that if the wifi connection suddenly degrades, the networking stack should just automatically switch over and try cellular -- are there complications?