Alsadius comments on Harry Potter and the Methods of Rationality discussion thread, part 26, chapter 97 - Less Wrong
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1) Same reason muskets trump trained knights and longbowmen. Even though heavy plate was actually effective against primitive firearms, and longbows worked more reliably and with excellent range, you could kit out a peasant with an arquebus for much less than the cost of mounting and armoring a knight, and a fraction of the training (you had to train for years to be able to fight effectively in mail or on horseback and drawing a longbow was an elite skill that required extreme muscle hypertrophy. It took a few hours to learn how to operate your firearm, and a few weeks to learn how to coordinate with other peasants.) Similarly, even if wizards were significantly more lethal and/or survivable than dudes with carbines, they'd be incredibly outnumbered.
2) In the Harry Potter World, combat magic is really weak. It's almost all short range and slow, often nonlethal, rarely provides area effects, and nobody really trains it. Automatic weapons have cyclic rates of hundreds or even thousands of rounds per minute, and trained operators can hit a target at half a mile or more. And that's just small arms. They wouldn't even need special anti-magic weapons, unless the wizards were extremely well organized.
I grant 1), of course. But wizards have shields that ought to be proof against handguns. My question was asked in response to the line "guns that will reliably break a wizard's shields".
'ought to' is often not the some as 'do' especially when the subject is Wizarding Britain.
Wizards aren't totally stupid. You shoot down a dozen or so, and the rest will remember their Bullet-Repelling Charms quickly enough.