I think there's a difference between spending a significant percentage on exorbitant salaries and the like and spending sensible and limited amounts on fundraising efforts. If a charity has an annual fundraising drive, they have to spend money on mailers (printing, postage, etc.). If they have a fundraising event, they need an underwriter to cover costs for catering, facility rental, etc. Those are dollars that are not going directly to the mission of the organization even though it certainly serves the mission. You could have an organization where 100% of donations go to the charity's mission, but no one will know about it and donations will be dramatically reduced. And even if you managed to get someone to rent a facility for free, or cater your event for free, or do your printing for free (very difficult in today's climate), those are still considered in kind donations and do not directly serve the mission.
Not saying a billboard is a good idea at all. Just saying that the analysis needs to be a little more nuanced.