But relegation wasn't 'the price of keeping Benitez'. Benitez obviously did not demand that Newcastle be relegated as a prerequisite to his decision to sign a contract.
Rather, relegation is the consequence of having a team that routinely demonstrated an insufficient amount of effort and commitment, which was led by a manager for three-quarters of the season who was not able to motivate them to better performances.
I suspect that most Newcastle fans would rather that their club had survived in the Premier League, even under the stewardship of McClaren, than suffer the ignominy of relegation. Benitez has not stayed because Newcastle have been relegated but in spite of it (and presumably because he is going to be paid oodles of dosh, of course).
'Relegation and Rafa is a good thing' is going to be a hard product to sell.