Spending money is necessary in order to speak to a large audience. You need money to rent space to use as meeting halls, or to buy advertising space like billboards or newspaper space, or even simply run a website. The more traffic, the more eyeballs, the more people impacted, the more it costs. Speech in the real world costs money.
The presidential election isn't won in the town square, where everyone can hear him gather to speak simultaneously. That might work for mayoral elections of small towns, but it does not work for a nation of 318 million people. And besides, who is going to pay to rent an auditorium for a town hall meeting?
The citizens deserve to hear their elected leaders and candidates speak, and it requires a considerable amount of money to reach such a large audience. (Note that donating air-time or website space or advertising for a candidate is tantamount to donating money.)
What is the serious alternative? Political candidates are limited in their ability to get their message out, based on where they can travel (no money for transportation), and the people they can speak to directly in person? How will democracy function at scale? Presidential candidates are pilgrims, traveling the country by foot? They'll have a hard time reaching a few hundred thousand people at best.
If we did not allow political contributions, and we did allow candidates to spend their own money on their campaigns, then only wealthy billionaires would become successful national politicians. Indeed, many successful politicians are extremely rich, like Mitt Romney (estimated net worth: $250 million), and candidates like Donald Trump rely largely on their wealth. Small-time candidates would have zero chance against them if contribution were not allowed, even while billionaires are spending their personal fortunes.
Now, to be a fair, a purely representational democracy could perhaps function on this basis. The people in a local area elect their local leader, who travels to the capital of a territory to mingle with other local leaders, and from them elect a higher leader, and so on, such that at each level campaigning is all word-of-mouth. But that's an idea that I think will fail in reality at the scale of the USA.