Handoff is handled by the client, not the access points, and the client tends to do a bad job. My iPhone, for example, is dumb enough to stay on a dying connection for like 30 seconds as I walk right next to another AP it could connect to, so I keep having to force it to rescan. My parents' house is a hostile environment for wifi signals themselves due to materials in the walls, so there are many APs, and the problem is extremely apparent there. Same with my college housing a few years back.
If you buy special wifi equipment with fancy tricks to help with this, it works a lot better (but still not flawlessly). Seems like those employ hacks to get around the deficiency in the wifi standard, like spoofing values or forcing clients to disconnect at a higher threshold, and the latter requires some tuning. Standard equipment like AirPort or whatever modem/router/wifi combo your cable company installs doesn't do the job.
Another issue is interference between APs. Pros are careful to avoid this, then they tell everyone not to set up their own APs. "Mesh network" technology avoids this automatically, though TBH I'm not sure exactly how they do it.
As a result, if my requirement is that I have at least 1 Mbit/s at all times, in my experience LTE has been better than wifi even in buildings with pro wifi setups. I've almost never seen my LTE fail, but wifi always has dead zones.
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It's possible. BT does support networking, I think IP at the lowest. BT 5 theoretically supports 48 Mbit/s. That's way more than enough for most. If I can get even 4 Mbit/s with Bluetooth but have perfect connectivity and easier setup, I'd gladly take that tradeoff.