The concept that created Bluetooth is that it would be short range and private. There only being one live connection follows from this. A 3 way splitter as shown above is effectively 3 bluetooth nodes in a box that plugs into the TV audio out hole that each set of phones can communicate with, one node per set of phones.
The advantage is fewer wires to angle and trip over.
To use multiple headphones from one socket, you need an adaptor. Quite likely the power to each set of headphones will be noticeably cut as more are plugged in before they tie themselves into a knot.