For instance, your very comment is published under a throwaway. Couldn't we say that your comment, being an attempt to influence us, shouldn't be anonymous? After all, perhaps you could stand to personally benefit in some way?
However, anonymity has a cost proportional to its impact. That cost is that the impact of the anonymous act will have no retribution. A person is more likely to act in a negative-sum way with anonymity.
Still, anonymity is essential because it protects the underpowered in their expression. We as a society have said that, on balance, anonymity with speech is good. And I think that's reasonable.
With money as speech, this logic is broken. Money is the purest form of power within our society. Giving money is an expression of power. The more money, the more power to express.
We then get all the negatives of anonymity with none of the benefits. What's more, as those with money can express a lot more than those without, the negatives are amplified.
Another way to think of it is that freedom of expression as a sort of democratic value because it equalizes power. Speech as money removes the equality of it.
To be more concrete, I believe that I can post anonymously but it would be dubious for me anonymously fund a lot of people posting here.