Can I? I show up extra early when I can (e.g. not a connecting flight) to make sure my carry-on is not bumped, but the only way to not have to worry about this is flying business, and that's more like a few thousand dollars extra, for cross-atlantic.

I may pay $25-$100 more. But not $3000.

yeah... I frequently fly with guitars. On Southwest, you can pay for early-bird check-in and get a nearly guaranteed A boarding spot. On American and United, you can pay $15 for early boarding. For international and generally on anything larger than a 767, overhead compartment space is rarely an issue.

$10k is not even very expensive yet. It's approximately just a camera body and a few lenses.

Regardless, paying extra $50-$100 on every flight sounds unreasonably high. $10-20 would be more reasonable.

You're missing the point. Nobody cares about the value of your bag.