There's no implicit order to hues, so it's hard to interpret meaning intuitively.

On a practical note, it uses every available colour, leaving you none for annotation.

For all of these reasons, MATLAB and Matplotlib no longer use rainbow-like colourmaps by default. And neither should you.

But I like rainbows!

People tend like things that are bad for them. Chris Jackson (Imperial, see here and here) and Bert Bril (dGB, in Slack) have both expressed an appreciation for rainbow-like colourmaps, or at least an indifference. Bert went so far as to say he doesn't like 'perceptual' colourmaps — those that monotonically and linearly increase in brightness.

I don't think indifference is allowed. Research with professional image interpreters has shown us that rainbow colourmaps impair the quality of their work. We know that these colours are hard for colourblind people to use. The practical issues of not being readable in greyscale and leaving no colours for annotation are always present. There's just no way we can ask, "Does it matter?" — at least not without offering some evidence that goes beyond mere anecdote.

I think what people like is the colour variance — it acts like contours, highlighting subtle features in the surface. Some of this extra detail is probably noise, but some is certainly signal, maybe even opportunity.

See what you think of these renderings of the seafloor pick on the Penobscot dataset, offshore Nova Scotia (licensed CC-BY-SA by dGB Earth Sciences and The Government of Nova Scotia). The top row are some rainbow-like colourmaps, all bad. The others are a selection of (more-or-less) perceptually awesome colourmaps. The names under each map are the names of the colourmaps in Python's matplotlib package.