The charities have severals reasons for doing this. {transparency / Tax etc} but it shuts it's income stream by doing this. I can understand the possible embarrasement it might cause, if donations they received from income derived from criminal activities... but some of these charities takes it to the extreme.
If they have a verified legitimate organization with a official webpage, why not place a Bitcoin address on the homepage and accept direct donations from the public?
That would be very impractical for larger charities.
Right now they can use Coinbase or BitPay which (99% sure on this) don't charge any fees to charities.
If they were to set up their own wallets it would generate a lot of extra costs, which could even outweigh the value of BTC donations. They would need to train X number of staff on how to handle bitcoins, establish safe storage system, register to BTC/fiat exchange (pay the fees there), probably set some sort of internal control/security system (decide who controls private keys etc.), not to mention extra work for their accountants.