As Andrew Thompson's comment hints, it's a matter of tankage mass vs the trifling extra mass of hydrogen. Tankage is no small thing; it's the main reason hydrolox ($H_2 / O_2$) rockets, despite their unparalleledunparalleled* $I_{SP}$, don't have much better performance than other liquid fuels with considerably lower specific impulse but much better density impulse (the— the hydrogen requires much larger tanks). Carrying oxygen efficiently in liquid form requires a pressure vessel and cryogenic handling (or else a much larger pressure vessel for compressed gas), and has extra safety requirements, since pure oxygen is a severe fire danger.
In particular, a large tank I found for sale contains up to 250 kg of lox at 2.3 MPa, and the tank itself is 151 kg, which is a really unpleasant 60% overhead (although this tank is not, of course, optimized for aerospace work). Compared to water, which can be contained in a much lighter tank and with an overhead of 1211.5%9% hydrogen, you can see that it's a significant penalty, even without the additional handling hassles and safety problems.
*Well, unparalleled among practical, vaguely safe chemical fuels, anyway. $H_2/F_2$, $H_2/Li/F_2$, and other weirder combinations have even higher $I_{SP}$, but require enormously complex and failure-prone tanks and engines.