You can convert live ellipses and rectangles to ordinary paths by using Unite in Transform palette, which is a nice hack. But the only way to convert live lines to paths — is through menu, Object > Shape > Expand shape. Three precise clicks with long distances run in-between.

Please, add button for this in shape properties area in Transform palette. There's plenty of space.

When path can be converted to live shape, change 'Expand live shape' button to 'Convert to live shape'.

And why there's no command for that in contextual menu still?