The Red Cross does not accept spontaneous international volunteers--and as far as I know, no other organization does, either.
In order to be an international Red Cross volunteer, you have to have extensive training in mass care--shelter operation, feeding, client tracking, and information dispersal--and at least five years of local and national disaster response experience. You also need to speak the destination's language fluently and have proven cultural competence and flexibility. If you join now and make the commitment of time (about 40 hours of training and one on-call week a month) and energy, you might be ready for the next U.S. disaster.
Now, let's talk about money. The Red Cross spends donated money in or near a disaster area, to purchase necessary supplies from local businesses. This means that these businesses can continue to pay their employees, who already affected by the disaster. Otherwise, they would lose their jobs on top of everything else that has happened. Donating money keeps people going in ways far beyond immediate supplies.
Also--the earthquake happened on Friday. The Red Cross and other relief organizations already existed, right? So before the disaster hit, they had offices in place to get information and coordinate their responses.
Relief agencies need stuff independent of any specific disaster.
Agencies need vehicles to get to disasters. These are usually vans and trucks. These need gas, oil, tires, inspection, maintenance, and insurance--all of which costs money. Agency offices need electricity, water, computers, Internet access, phones, phone service, printers, paper, toner--and people. People need to be paid living wages and have healthcare insurance in full-time jobs. (You want that, right?)
All of that already had to be paid for, so when disasters occur, the agencies are ready. Without unrestricted donations not tied to any event, relief agencies cannot have any of these necessities--and can't respond as effectively as necessary.