Among other pros of raising private donations:
Overall, political advertising costs money (a LOT) since it not only has to compete with other political advertising but with all the NON-political ads out there. This inflates the prices of advertising to the point that no publicaly funded candidate can afford to advertise. Which in turn gives an incumbent a 100% guarantee of re-election, which is obviously bad for democracy. With no incumbent, the edge goes to a celebrity, or someone beloved by the media.
In other words, "adequate to run their campaign" is not something we have enough public money to spend on, for any definition of "adequate".
A candidate that is opposed by the 4th branch of government (media) has ZERO chance of getting their voice out without raising a substantial amount of money. Leaving aside the sure-to-generate-debate issue of whether MSM in America is liberal (but if you care, look who major newspapers editorial opinions endorsed recently), the proof is in the pudding: Media-organized debates have uniformly excluded less "major" candidates of all political persuasions.
As far as the cons, "beholden to their campaign contributors" is a nice phrase to use around the coctail table, but there needs to be some research to show that it is actually true.
FiveThirtyEight ran a post last year that raising spending on ads in a non-edge case (e.g. when both candidates are already somewhat known) by 100% merely adds 1% margin to the vote. And for any campaign other than national Prez election, advertising is the biggest expenditure (for Prez, get out the vote operations and organizing take money too).