Why aren't the Hawaiian islands a continuous strip of land?
Don't be mislead by the subaerial part, it is actually a ridge on a large scale but neither the lava production rate nor erosion rates are constants. That leaves the ridge with higher and lower parts, as well as gaps. Furthermore reef building biocenoses change shape and appearance of the eroding volcanic edifices.

Hawaiian (and other like for instance the Canarian) volcanoes go through stages during their lifetime with different production rates and magma composition. Connections to the magma chamber(s) may remain in place for some time while the volcanic edifice moves relative to the magma source(*), until it has moved so far away that rising magma seeks new ascent channels to rise and deformation forms new dykes and cracks and so it may erupt from different vents, and that from a possible complex and subdivided magma chamber(s) fed by the plume underneath.

That process may leave an appearance of single detached volcanoes like e.g. M. Loa and M. Kea, but they are just similar things at different stages. Many volcanoes never reach a subaerial state and remain submerged, contributing to the appearance of detached islands.

(*) i would say, whether it is the plate that moves or the plume or the connections between plume and magma chambers is mostly irrelevant. Base argument is that the rate is not constant and eruptions may seek different paths during time. As to the exact why and how, that's ongoing discussion.