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In this case there's no advantage to using logistic regression on an image other than the novelty. Logistic regression is excellent for feature explainability, but you can't explain anything from an image.
Traditional classification algorithms but not deep learning such as SVMs and Random Forest perform a lot better on MNIST, up to 97% accuracy compared to the 88% from logistic regression in this post. Check the Original MNIST benchmarks here: http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/#
Pytorch includes a simple neural network example for the MNIST data: https://github.com/pytorch/examples/blob/main/mnist/main.py
It only takes a few minutes to train with default parameters and will have >99% accuracy on the MNIST test set.
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