Whenever I fly, I'm always slightly worried that my climbing gear doesn't arrive, but apart from that, last time I traveled, which was a few days ago, it was still perfectly fine to bring everything I need in my checked luggage. I've never doubted that items like ice tools, crampons, ice screws, carabiners and so on are easily recognized for what they are using X-ray machines. To be precise, my last flight was directly from Ecuador to the Netherlands, but previously I've flown via the USA as well.
To get it all transported safely, I stuff all my climbing gear in a medium to large backpack, together with my other luggage, and the pack always ends up completely full so nothing could possibly shift around and get damaged. After that, I stuff the pack in an even larger duffel bag. First of all, the duffel prevents the straps from the pack from being hung up on anything while in transit, but it also protects my backpack. After arriving on my destination, I use the duffel bag separately.
The most important exception I make is for my mountaineering boots, which I take into the cabin - it could be time consuming to find suitable ones to rent or buy some on the spot, should my stuff be delayed or go missing. That is, I just carry them, while walking on sandals, but if anybody would complain about exceeding my carry-on limit, I would put on the boots and put the sandals in my carry-on bag - problem solved. Never had to do that though.
By the way, my carry-on tends to be on the big side. It's the medium sized backpack that I like to use when I'm climbing, and I fill it up with expensive or hard to replace things like a down jacket, mittens, rain gear, plus whatever didn't fit in the big pack anymore. If I would ever be called on it being too big (usually, it does exceed the official size limits), I could always wear some of the stuff (I'll just suffer being really warm for a while) after which I could easily compress the pack into an acceptable size.