Tile cracks on a convex edge
This is a tough one. Very odd to have that "cube" adjacent to the tub with a cabinet so close. The cabinet should have been pushed up against the tub and the cube/cabinet gap bridged, waterproofed, and tiled, so there would be no gap.

If the problem were just aesthetic I would say use some porcelain repair, it comes in a bottle with a paintbrush type applicator on the cap. Actually, the stuff dries hard and thin and might actually help with the water penetration issue that is your concern.

Silicone would work too, I would not worry about water pooling because of it. You are actually better off with water pooling where you can see it and dry it up, as opposed to it running off into that small gap and pooling back in that corner on the floor, which will eventually cause you big problems with the floor substrate.

Why is the damage occurring? There seems to be no reason for it. Sometimes bullnosed or V-cap tiles (those that wrap around an edge) crack along the edge due to expansion/contraction or improper bonding, but yours seems to have a grout joint along the edge. The real fix is to tear it out and replace it, and it does not look to be easy because of the location.