The rules seem to say that I must have at least one card for each Mode in my new tableau.
This is (sort of) the rule for a failed topple. Culling down to (at most) one card of each mode.
For nation building, you must pick up your whole tableau. You can then discard any number of cards without penalty. Then play resumes.
If this is correct, I will put my weakest cards in the tableau and keep the strongest cards in my hand in order to get more units in play.
What's wrong with this plan?
Nothing at all, mechanically. You might want to keep a higher ranked card in your tableau to give you access to a stronger action right away.