It doesn't seem strange to me (of course, strangeness
is in the eye of the beholder).  I've found it useful to have
most of my GUI's extend JApplet, but also to write a simple
main() that creates a JFrame, adds the JApplet to it, and
calls init() and start().  This provides a bare-bones but
adequate browser-like environment for the JApplet, and gives
me the flexibility to use it as an actual applet or as an
application (usually, as a Java Web Start application).

    There's very little that the two modes of execution need
to do differently, once initialized.  The in-a-JFrame version
might want to manage a window title that the applet wouldn't,
maybe a few menu items (like File->Exit) are present in one
mode but absent in the other, ...  By and large, the JApplet
"just works" no matter which way it was actually started.