In my class, which is mostly principle-based anyhow, we spend a lot of time on partner practice exercises for natural movement, structure and connection. But they mostly derive from or involve aikido basic technique.
I think you have to dive into practice or new students will not feel they are learning what they as beginners feel they are there to learn. I have always favored an integrated approach.
In aiki-weapons, many instructors dive right into teaching the kata. Because I am myself not a kinesthetic learner, I tend to like to start by teaching holding the jo or bokken, then drilling on the basic movements - footwork, thrusts, shomen cuts, etc - doing repetitions moving across the dojo using the mirror - before starting to teach the kata. Unlike many who teach the kata as a whole, I like to only teach newbies a few steps at a time.
No suburi? I suppose it is expected that the student practice suburi on their own at home. The results of which become instantly apparent when attempting kata. Actually, here, suburi is on the test requirements for the first few kyu grades.