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One issue with SVD is its significant time complexity compared to, for example, the Discrete Cosine Transform used in JPEG

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SVD is used more for mathematical elegance than practicality (like ordinary least squares)

In data science most traditional usecases for SVD are superceded by other algorithms (UMAP is especially popular these days).

Can you build image compression on UMAP?

There are loads of numerical algorithms where the SVD is the tool of choice because of its particular optimality properties.

Right, like OLS.

Don't get me wrong -- they're great tools. Especially OLS for analysis has this whole framework for understanding errors you will not get in models fit using maximum likelihood methods.

But as a final usecase for a product there's generally better out there.

I think you're mainly thinking of machine learning and data science applications, and so your perspective may be a bit limited. But, of course, you didn't actually give any explanation of what you mean other than mentioning ordinary least squares. Would you like to elaborate and back your point up?

In computational science and engineering, there are many applications in which the SVD is a very reasonable and good choice. Some examples: fast direct solvers for integral equations, model order reduction, solving inverse problems, etc.

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