Time-division multiplexing. The router has to wait for everyone else to stop using the band—and then take that opportunity to tell them to all shut up for a moment—before it can say anything. And it has to finish what it was saying before it does even this, because it has guaranteed its clients it would send packets of certain lengths by certain deadlines. (Plus QOSing: as the person owning a router, you almost always want your established wi-fi connections to take service priority, so that your phone coming gradually into range as you get home doesn't kill your family's downloads.)

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.)