The resistor may be removed if the signals at ports 2 and 3 are in phase and have equal magnitude.
The resistor works to match the 2 and 3 port also to provide an isolation between them. So if you remove that reflected waves may come back towards input and degrade the input performance.
As the two previous writers say, the resistor is to help reduce the effect of reflections from the output ports. If you take away the resistor then any reflections will bounce around the system and can make it very "lively" and difficult to tune or balance, because the signal at one output will depend on the match at the other output. The resistor reduces this. If both reflections are the same then the resistor doesn't do anything and the reflections go back down the input, but in all other cases the resistor carries current and reduces the amount of reflection that goes from one output to the other. If you are going to miss out the resistor then the divider can be made smaller. If you circuit is lossy you may be able to get away with it because the reflections will die away before they get somewhere you don't want them.
Most conventional base station arrays incorporate corporate feeds with resistorless Wilkinsons. This saves space and shortens the overall path from input to antennas. Antenna matches must be very good such that reflections back into the dividers are kept small. As mentioned above the resistors provide isolation and balance. Frequency response of S21 (input to one leg) under ideal loading is 3dB plus losses. Without a reasonable match on the antenna ports you will see significant ripple across the frequency response resulting in unbalanced outputs.
I think it is true to say that a Wilkinson divider without a resistor is not a Wilkinson divider, but just a divider. I think Wilkinson's aim was to reduce the cross-talk through dividers.
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