Yes those are what I always called a repeater in the past. Now with all the companies trying to undercut each other on price you have the market flooded with the junk calling themselves repeaters. The only place you even can think to find a true "repeater" is in some of the commercial equipment and the manufactures of outdoor systems. But when even a fairly educated customer see $350 or more compared to $29.99 which do you think they are going to choose. They do not want to spend the time to learn why the more expensive unit has advantages they just believe the marketing hype.....just like the sheep who buy "new and improved" bags of chips where all that is improved is they reduce the content and leave the price the same.
The key reason the cheap repeaters are so bad is they retransmit the signal into the same exact channels they received the transmission on. The huge problem occurs because of exactly the reason the repeater was installed in the first place. Machine A can not talk to Machine B because they cannot detect each other radio transmissions. So I put a repeater in the middle. Sounds good in theory now the repeater can hear each machine and relay the signal. Problem is there is no transmission control in wireless. They listen and if they hear nobody transmitting then they transmit. So now since machine A and machine B cannot hear each other they assume they can transmit at any time. Problem is the repeater now hears both transmissions overlapped and destroyed. So the more the data that is transmitted the more you get degraded. And this does not even count the 50% loss that the end devices get when they actually wait because they hear the repeater transmitting.
As you could expect with it this bad already if you were to daisy chain repeaters it becomes unworkable.
So if we look at using a true repeater that users 2 radios one for the back haul to the main router and one to talk to the user. It is actually cheaper to buy 2 routers to do this one acting as a client-bridge connected to a second running as a AP. Lets say I had a central building and I was going to connect a bunch of remote buildings. I would put in a outdoor network to connect to the main building say on the 5g channel and then repeat it into the building using the 2.4g channel as a AP. This type of design works well. The critical part is all the remote building must be able to receive good signal from the main and then still be able to reach the the users inside the building.
So IF you can find a location on each floor that can see a central location you could repeat the signals into the rooms with this type of repeater. You are in effect using one frequency replace the ethenet cable to the AP. If you can cable part of it you could build multiple central locations but you are in big trouble if you try to cascade repeaters even on different frequencies.
Bandwidth is the largest issue that is killing wireless. Wireless shares extremely bad because of its no centralized control of who transmits. Used to be no issue when they users were checking email or logging into their work to do some simple stuff. Now especially in a hotel environment everyone is streaming hidef video, running skype video chat, playing large games. A video stream is one of the worst thing since it pretty much constantly is transmitting. You get even 5 people doing this and it degrade rapidly even on the newest and fastest wireless.
I would be thinking maybe 10 rooms/AP and this is assuming cabled backhauls to the central switch. Using radio back hauls would be the same as saying now instead of each users trying to use 4m each I now have combined my users in huge super users trying to eat 20m each all from a central AP.
Hotel users will tend to use more bandwidth than say your coffee shop. It is much more likely for them to stream a movie especially in hotels since the hotel is going to charge them a huge fee for anything on the TV.