Ruddy nuisances. But so are some teenagers.
Yes, pigeons are a pest. However, if you shoot one, another will only move into its territory, so you're always going to be back at square one.
Also, you can't be there all the time that the pigeons are feeding; and how do you know you shoot the culprit? Are you just going to shoot ALL pigeons, guilty or not, on your plot or not?
I don't agree with shooting (you might have sussed that) and I would not be happy if you shot pigeons that were on my plot. I may choose to pellet slugs, but I'm sure you'd be unhappy if I scattered your plot with slug pellets, just in case 'your' slugs were the ones munching my veg; or came on your plot to chop down your weeds incase they seeded themselves onto my plot.
If you want to reduce the pigeon population, their food supply needs to be restricted, and possibly their nest sites. That means not feeding them with crops or with bread/seed on birdtables.
If your intention is to protect your crops, you need to net them. although it's not as much fun as blasting dumb animals to death, I grant you
PS. We're not falling out about this, I just wanted to put my two'pennorth in.