According to Siekmann, from a legal point of view, the abolition of cash or restrictions appears to be an infraction of EU law and of German constitutional law. Depending on the details, this also holds true for mere restrictions.
For Siekmann another argument for the constraints is probably most important but not disclosed so much in public: “Making the use of cash more costly or abolishing it completely may finally bestow upon the present ‘unconventional’ monetary policy the effectiveness it appears to be lacking so far”.
IMFS Working Paper No. 108
"Restricting the Use of Cash in the European Monetary Union"
(PDF, 292 KB)