Is there some reason not to use
   <xsl:template match="Paragraph[@stylename = 'Body']">
     <xsl:apply-templates select="./TextRun/Text/@value"/>
   </xsl:template>
?

Not that I can see ... though the "./" is redundant.

Right. Good point. I was just copying from the OP -- all I did was
s/value-of/apply-templates/;. :-)

What led you to believe this was verboten?

Only that Gerrit and Michael had raised other solutions that, IMHO,
seem a little less XSLT-ish. So I thought maybe there was some
"gotcha" I had overlooked.