Currently this is the state fo the Social Icons block when inserted:

Problems I see:

• the instructional text contains the word "Click" which makes you assume you can click to add. This is not the case. Moreover we shouldn't need to rely on this text.
• the + plus icon is aligned to far right and is disconnected from where the user is naturally drawn. It sholud be where the instructional text is and the text shouldn't even be there.

Other suggested improvements:

• consider a placeholder state whereby a placeholder icon acts as the inserter. When you click the icon it brings up the block inserter to pick your social platform.

cc @richtabor who is looking into editor polish and may have other ideas for improvements