Different estimators have different penalty param names, and also have different meanings:
alpha param in Lasso is a regularization strength (for bigger values of alpha regularization strength is ascending)
C param in LogisticRegression and SVM is a opposition of regularization strength (for bigger values of C regularization strength is descending)
Besides that, plot_stability_path generates different plots for such estimators (shrinking on left or right sides of plot).
Using 1/C syntax it's possible to synchronize these meanings and make it more intuitive.