Yes it's by design, we have not used any 'menu' except we have styled the 'links' skinobject and this is because of a couple of things.
That's how the designs were found in the 'free templates' that exist around different sites - we were just converting them to be for dotnetnuke skins and passing them on to the community as quick as possible.
By design, it doesn't show the host and admin menu since it's just using the skinobject you would normally use for breadcrumbs or links.
So, to get around this, we put in a 'visible to admins only' menu which allowed you to still access the pages when logged in.
We are working hard on making 'compliant' skins for dnn and we don't use solpart or dnnnav menu at all - we only use the snapsis menu.
So, for us to make these skins compliant, and use what was available on the internet for us to convert as quick as possible, we tested the links skinobject and decided that for free, it was an excellent choice.
You would you have apply the solpart or dnn nav menu yourself since as much as we love dnn, we feel we don't have the resource here to provide good, free skins, with dnn based xhtml compliant menus and they take far too long to configure.
You could also consider purchasing a snapsis menu to put into your skin. It's a very inexpensive choice to get something that is so good.
Life is too short to be unhappy!