Why does babel not work in Tikz?

The reason is that TeX doesn't hyphenate the first word in a paragraph. Inserting \hspace{0pt} for example would enable hyphenation, because then the word is not at the very beginning:

child {node[concept] {\hspace{0pt}Unterschiedsschwelle}}

One can abuse the font= key in the node's options, to add the \hspace{0pt} macro at the beginning of the node. However this overwrites previous font keys, if present.

child {node[concept,font={\hspace{0pt}}] {Unterschiedsschwelle}}

In order to preserve the existing font keys, you can define the following in the preamble

\makeatletter
\tikzset{add to font/.code={\expandafter\def\expandafter\tikz@textfont\expandafter{\tikz@textfont#1}}}
\makeatother

then use it as

child {node[concept,add to font={\hspace{0pt}}] {Unterschiedsschwelle}}
child {node[concept,add to font={\hspace{0pt}}] {Unter\-schieds\-schwel\-le}}

to obtain