As a counterpoint, I'm involved with a private foundation that donates a total in the mid-six figures to various organizations each year (foundations like ours and probably Dropbox's have to donate 5% of their assets annually), and most of our donations are restricted in one way or another.
The way things usually go is we get interested in an organization and ask them if they need funding for any specific projects or initiatives this year, they send us a list of options, and we choose from the list. Usually we'll get an email later on about how the project went. If we don't care for any of the options but we still like the organization, we might make an unrestricted (albeit probably smaller) donation instead.
We do it this way for a lot of reasons, but one is that nonprofits can be as flawed as any corporation and in many cases they have all kinds of stuff they'd love to spend money on if they could that isn't directly related to their mission, or rather is related enough that they can book it as "program expenses" for the purposes of maintaining a five-star Charity Navigator rating when a reasonable person might look at it and see some amount of wastefulness. (That probably sounds more cynical than I actually feel about it, but it's a real issue.) Examples would be things like fancy office spaces and parties, questionable executive travel or compensation, optimizing for metrics that make the CEO sound good but aren't as impactful to the core mission as what they could be doing, etc.
Anecdotally, I'd say this is more commonly an issue with mid-sized organizations: huge charities usually have a big nest egg (like an endowment) to cover regular operating expenses, while very small charities are more likely to be entirely staffed by volunteers and thus have negligible overhead.
Anyway, we basically just want to know where our money's going. I can't speak to how gigantic foundations operate, but I'm sure there are a whole lot of individual donors and smaller foundations who do things the way we do (with no desire to claim credit).