The important point is to save the person—not to do something that looks heroic.
If the rope method didn’t work or wasn’t available, jumping in might very well be in order, but it is much more risky to both parties—not only might the rescurer be drowned (most likely unintentionally by the first person in), but a drowned rescuer really isn’t much use.
No sh!t Sherlock. That's not what I meant. Calling what he did "heroic" is a misuse of the term.
Rescue of the non-swimmer often requires subduing the victim with a hold from behind, to avoid becoming subject to their panicked behavior. This requires a strong swimmer to make way to shore encumbered with one or more limbs involved with a holding action. Much less difficulty for a solo rescue swimmer, if the drowning victim has ceased struggle, as long as effective CPR can be immediately applied.