Large operators have always seems strange to me, sometimes their meaning is based on the symbol and other times it has no correlation. For instance, the summation (sigma) has no relation to the meaning, while
$\bigcup_{a}^{b} x_a = x_1 \cup x_2 ... x_b$
The big U is just a "summation-like-instance" of the small u. Do all operations have large counterparts?
A large plus symbol (or product symbol), would graphically look very bad, especially if you try to put indices on it. However large version of circled plus or times, are used: $\bigoplus$, $\bigotimes$.