Around the page I edit modules constitute the primary page. Really there's no requirement for any component available.

I can not remove jdoc in the template because other area of the site requires it.

I question what's the best answer for that problem: for primary page I want one template however for others another.

As far I've labored with joomla internals rarely with back-finish and so i guess my understanding don't have any this department.

Any hint how to accomplish this?

That you can do something inside your template like:

<?php 
    $menu = JSite::getMenu();
    if ($menu->getActive() != $menu->getDefault()) : ?>
        <jdoc:include type="component" />
<?php endif; ?>

That will disable the component position when around the default [home] page