Why do some SMD electrolytic capacitors have platforms?

Those capacitors are really made similarly to the cylindrical radial lead through-hole capacitors. Two connections come out through a rubber bung (in an aluminum case that is crimped at the bottom to form a seal) and those leads are bend to form SMT leads.

From this Nichicon website (a conductive polymer type is shown, and conventional electrolytics are similar):

The plastic base is just there to provide physical support for the capacitor can so it doesn't flop around too much on the leads.