Why can a broad, hot mantle plume head produce a huge basalt province?

Answer: It flattens under the plate and melts across a wide area.

It rises through one narrow vent and feeds a single volcano. — This gets the geometry backward: a narrow conduit fits the plume tail or a later hotspot track, not the first broad head. The head can spread like a pancake underground and load many vents across a region. A single narrow vent would leave a much smaller volcanic feature.

It flattens under the plate and melts across a wide area. ✓ — A plume head is broad compared with its tail, so when it reaches the base of the lithosphere it can flatten and melt over a wide area. That broad melting can feed many vents and intrusions, leaving a large basalt province rather than a single cone. The later narrow tail is what can make a hotspot track.

It follows a seafloor trench, where subduction adds water and makes melt. — This borrows the right idea that water can help rock melt, but places it in a subduction zone. There, one plate dives under another and fluids trigger arc magmas along a plate edge. A plume head is an upwelling body that reaches the underside of the lithosphere, not a trench-guided melt.