John Higgs wrote a brilliant book [1] about the band KLF (who famously burned a million pounds). I highly, highly recommend it - even if you know nothing about the band (or care to), it's an incredible read.
The KLF have long been heroes of mine, but the book covers everything from the meaning of creativity, 60s counterculture, art history, music and much more.
After reading I was directly inspired to cause as much good chaos as possible.
John Higgs (and the KLF) are treasures.
Cash is a liability of the central bank, yep. Destroying it removes a liability from the bank's balance sheet, increasing their equity. As others have noted, destroying cash is equivalent to returning money to an arm of government.
As you say, if people destroyed cash on a regular basis, it would be deflationary: the central bank would respond by lowering interest rates. When the increased equity was eventually booked as profit, it would go back to the government, who would (presumably) spend it.
Both the lower rates and the increased spending are inflationary, so in the long run we might expect that the system would balance itself out.
A lot of people seem angry at them for burning the money instead of giving it to charity. No one would be angry at them for spending it all on something dumb (e.g. a boat), and this way everyone else's money gets worth very slightly more.
Incidentally, Bill Drummond's 45 [2] is a great read too. Especially for the creatively minded person.