Same reason you'd host any sort of expensive party. To look cool and feel cool. A lot of international politics make a lot more sense when you remember we're all in high school.
Actually, I was very skeptical about the London Olympics before the event. However, I thought the whole thing went splendidly and arguably did give the whole of the UK a bit of a lift in national morale just when we really needed it.
Compared to other megaprojects that we seem to be happy to splurge taxpayers money on (e.g. silly aircraft carriers) it actually seemed pretty good value for money.
Current estimate for the QE Carrier project is £5.5 billion, or about 60% of what the Olympics cost.
In comparison to a few weeks of enabling professional athletes 'perform' , the carriers should give at least 45 years of service life. A tangible contribution to UK security, rather than just a TV event.
I'm not a fan of how the carrier project has been managed but to say it's worse value than the Olympics surprises me.
Compared to other megaprojects that we seem to be happy to splurge taxpayers money on (e.g. silly aircraft carriers) it actually seemed pretty good value for money.