Why don't all feature selection methods in sklearn allow specifying desired variance explained? Why don't all feature selection methods in sklearn allow specifying desired variance explained?

sklearn.decomposition.PCA does allow inputting a percentage of variance that one wants to be explained in place of n_components. However other methods such as SparsePCA expect the user to "know" how many n_components he/she wants to take.
Because PCA is just one of the feature selection methods, don't expect others to have a tractable computable formula to specify ahead of time the optimal number of new features.
I suggest to start reading on Representation learning, and what we mean by latent variables.