"300 dpi" is a number that someone, somewhere pulled out of their behind and everyone started repeating without questioning or understanding it.

First of all, you're rendering in ppi not dpi. Unless you're a printer, and by that I mean the device (not the profession) you will never get to see an image that's in dots instead of pixels. In traditional printing, you worry about lpi. Magazines like Playboy are printed at 150 lpi, magazines oriented less at photography have an even lower resolution. If your 24" by 24" prints are being looked as closely as the centerfolds and are supposed to be in higher quality, then 300ppi are what you want.

I have several high quality prints in my living room as decoration, from photos friends have taken. The prints are 29 inches wide, from photos at ~3000 pixels wide (= 100 dpi). You have to get really close to them to notice the pixels, in regular viewing distance they look perfectly fine.