Why should a font list always end with serif, sans-serif or monospace?
Because it is the only CSS specification guarantee that text renders in a font from the right category; without a generic family at the end, if every named font is missing, the browser's behavior for choosing a final font stops being predictable across implementations.
Is monospace useful for anything besides code?
Yes, for any tabular content without an HTML table, like receipts, statements or numbers aligned by column in plain text, because the fixed width of every character reproduces the visual alignment that a proportional font can only fake with manually calculated spacing.
Are cursive and fantasy, the other two CSS2 generic families, worth declaring?
Rarely for serious product work: cursive and fantasy resolve to highly inconsistent decorative fonts across operating systems, so most professional style guides avoid both and concentrate their fallback strategy on serif, sans-serif and monospace, which behave far more predictably.
Why was Georgia picked as the serif example instead of Times New Roman?
Because Georgia was designed in 1993 specifically for low-resolution screens, with reduced stroke contrast and a taller x-height, while Times New Roman was optimized for print in 1931 and tends to look thinner and tighter on ordinary monitors.