Thanks Wolfgang. I could even have sections in the TOC  with '\setuptexttexts[{\placerawheaddata[section]}]'.

However, how can I start a new page at each new section? The 'page=yes' pair does no longer work with your solution 'placehead=hidden' (since the head is not placed I guess). I also tried 'before=\page' or 'after=\page' without more success. Here is a minimal example showing the absence of page breaks though I specified 'page=yes' (the section numbers are also mismatched but if one puts manual page breaks they match again, so it's not really a problem for me):

\setupheadertexts[\namedstructurevariable{section}{title}][]

\setuphead

  [section]

  [placehead=hidden,

   page=yes] % <-- This key does NOT work.

\setuphead

  [subsection]

  [placehead=yes,

   before={\blank[line]},

   after={\blank[line]}]

\setuptexttexts[{\placerawheaddata[section]}]

\showframe

\starttext

\completecontent

\dorecurse{2}

  {\section{My section}

   \dorecurse{2}

     {\subsection{My subsection}

      \input knuth}}

\stoptext