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You certainly could. But XOR gates are built out of AND, OR and NOT gates.
x XOR y = ( x OR y ) AND NOT ( x AND y )
and AND, OR and NOT gates can be built directly out of transistors, but I don't think XOR gates can be. (I could be wrong; I'm not an electrical engineer.)
As per the Truth Table of the OR Gate and XOR Gate, the first three rows are (0+0=0, 0+1=1, 1+0=1) common to OR Gate and XOR Gate. The last row is entirely different from each other. That is 1+1=0 in respect of XOR Gate and 1+1=1 in respect of OR Gate. The last row is not acted in Full Adder. That is both the Carry of 1st and 2nd Half Adder, never become the same as 1:1. That is whenever the Carry of the 1st Half Adder is = 1, the Carry of the 2nd Half Adder will become = 0. That is the resultant '0' (1+1=0) of the XOR Gate may be the Sum, and the resultant '1' (1+1=1) of the OR Gate may be the Carry.
The XOR Gate is the combination of 2 NOT Gates, 2 AND Gate and 1 (One) OR Gate. However the XOR Gate is different from OR Gate.
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Correction to Question:
That is the last row of the Truth Table (1+1=1) of the OR Gate is not acted upon in the Full Adder Circuit. Hence why should not use another one XOR Gate in the place of OR Gate in order to add the output Carry of the two Half Adders?