For about 90% of candidates, work experience is critical to making business school worthwhile. There are a few who maybe warrant admission immediately, but they too lose some of the values.
From completing your undergrad and getting a job, you begin to know what you do and don't like about careers, jobs, environments. Not even the greatest undergrad straight into school will get that, and it is lost value. You can only do school once, and you are wasting a bit of the value you have on knowing what you want to avoid.
I am sure there has been another few threads on contribution to class, and how more experience normally brings more value to the discussion (this is shown further by Exec MBAs, where they do not even grade classes because the contribution is incredible and hugely important beyond quizzes).
If you want to stay in education straight from undergrad, I don't think an MBA is the right thing. There are plenty other more targeted, academic masters that fit the bill better. That's my feeling, anyway.
Get the best GMAT Prep Resources with GMAT Club Premium Membership