Will the H and L have to learn each other's passing mechanics, and switch at halftime? That doubles the complexity and increases the risk of error. In addition, there's no opportunity to conference and make adjustments at halftime. It'll be too late; the mechanics to be discussed won't be in effect in the second half.
Or perhaps we keep letting the H drift on a pass, foregoing the advantage of letting the L see the down box as a point of reference. Either way, there's a cost. And even still, the mechanics cannot be completely identical as before. An 8-yard buttonhook on 3rd and 8 is handled quite differently on an experienced H's side than on an experienced L's side.
Furthermore the ball rotation mechanics also change at halftime. Think why the "extra" ball is always on the F's side. It's because that's the side where the officials aren't busy with the chains after a COP. But now that's the S's side half the time. So does the S handle the extra ball in the first half? Or does that stay with the F, putting the extra ball on the same side as the chains? Either way, it makes one thing or another more complicated for at least four officials and four ball persons. This could jeopardize game flow.