Do they work? To varying degrees. You’ll extend your range at the cost of speed and latency, mostly because of how extenders work. Unless you have them wired for the back haul that is; that’s called roaming though (IIRC). The nice thing is you can add an extender to an existing network.
Mesh routers are a better bet, though they are more expensive. The best ones will have little performance difference at the mesh points than at the base station.
I have Amplifi HD at home. It’s pretty decent, though there are better options out there.
I moved to a new 100+ year old house about a year and a half ago. I had my Airport wifi basestation at the front end of the house in one of the bedrooms. The signal did not reach to the rear of the house where the TV was. Not a massive house by any means, the signal was obviously being obstructed. I first tried getting a few Apple airport express stations to extend. Was simple to setup but the speed was severely down at the one end of the house compared to the other. In the end I opted do direct connect my Apple TV with ethernet through a powerline network adapter. This basically uses your power sockets as a network connection. Surprised how well it work and the speeds I get out of them 100+ mbp.
Have not used the mesh network but from what I have read this is the best solution to getting a larger wifi coverage.
“If you are neutral in situations of injustice, you have chosen the side of the oppressor. If an elephant has its foot on the tail of a mouse and you say that you are neutral, the mouse will not appreciate your neutrality.” Bishop Desmond Tutu
Used a powerline setup in this century home (masonary interior walls) with grat success until the first electrical storm totalled the adapters.....
Actually, in defence of the powerline extenders, any nasty lightening storm can kill almost any consumer electrical device, and especially if they have any wires attached. They can act as a nice antenna for the lightening!!!
I'm sure such a device would be quite good for helping normal power surges, but lightening strikes can have millions of volts and a huge amount of amperage current so I would tend to doubt any real benefit in such circumstances, especially with any close lightening strike. But I'm not an electrical engineer either.
But we leftcoasters tend to be more immune to such strikes compared to other patrs of the country.