history is littered with stories of t/o's that weren't quite...

history is littered with stories of t/o's that weren't quite high enough to convince shareholders to sell out, leaving an annoying 10%+ minority stake still listed.
This leads to greenmail, extra costs, continued public disclosure, exposure to rating agency ratings etc. etc, all of which you hope to avoid by being private. To that end, shareholders benefit from a bid for their stock at an elevated price that is at a higher enough premium to encourage selling...