"I don't know if it is possible that the money can be handed straight to the central government without being taken away parts by the lower levels"
Throughout history, many countries had the system of the central government and regional governments.
Regional governments had to pay fixed amount of tax to the central government.
Regional governments would collect taxes from their territories, and use it to sustain themselves and pay tax to the central government.
Central government would determine the exact amount of money that a regional government has to pay.
Also, central government would make public declaration about exact amount of money each citizen has to pay to the regional government.
This helped a lot with fighting corruption.
Regional governments who wouldnt pay the demanded sum of money would face penalty, removal from power, or maybe even death.
Now, in case of voluntary taxes, this would be hard to apply 600 years ago. This is simply because any regional government can lie about the amount of donated money. It would be very hard for the central government to figure out who is lying.
Central government could deny services to the regional governments who dont pay enough, and that could maybe work. Still, countries with mandatory taxes would have great advantage.
Today we have computers who can make list of everyone who donated and the list could be publicly available for anyone to see.