"We've put our pack in a beater suitcase and put the poles in there as well. We stay in a hotel the first night, leave the suitcase there with the bellhop, and pick it up on the way home..."
Different techniques for different trips; my wife and I have done this one a couple of times, and the hotels seemed to have no problem holding on to rather low volume stuff --- something like a cheap and relatively thin duffel bag works great in that way. So IF you start and end your trip in the same town, that can be a fine approach, though some towns or cities are easier than others to leave stuff behind in..
Typically, however, I do a linear trip where I fly back home from a different airport, without having booked passage ahead (for longer trips it's challenging to predict an end date that doesn't leave you either rushing or waiting around at the end).
A real beater suitcase or duffle, one perhaps purchased cheap at goodwill or the like can simply be left at a local goodwill or equivalent. I've got one or two such at my house from trips friends have made where we start in my region.
Or as I think someone suggested, package everything in a box as checked baggage, and dispose of the box on the other end. In this scenario, I can't necessarily repeat that trick on the way back home, so I like to use an older backpack, one that I'm less concerned about damage/loss to if it gets messed about en route back home at the end of the trip.
The problem with these approaches is that on the way home it's often not practical to try to get a box and tape or another "burner" suitcase or the like.
I've had reasonable luck with yard waste or contractor plastic bags. Coming home from Florida recently I didn't have a contractor bag, so just used all three very thin yard waste bags I had with me over my aging ULA pack. At the airport I pulled the yard waste bags up to close to the top of (this top-opening) pack, and used the little bit of duct tape I generally carry to tape it to the upper pack fabric, above all of the strapping. That way, the baggage handlers have something to potentially grab (strap across the top), and TSA can open the pack without taking off the pack-protective yard waste bags. My trekking poles collapse relatively small and put in diagonally they worked okay --- wadded/wrapped my bandanda around the slightly protruding pole tips and put rubber bands around to keep that in place. Anyway, this worked fine, and is sort of my default, fall-back approach when nothing else works. The catch is, it seems like every airline or maybe airport (?) is different. I've had at least one experience (don't remember now if it was plane, train or bus) where I was told that the outer plastic had to come off before I could check my bag.
Flying places in the U.S., I've on occasion shipped my stuff ahead to a starting-the-trail hostel or trail angel or a local friend. Since airlines charge to check baggage anyway, this isn't necessarily a lot more expensive, and I generally feel more confident this way that my stuff will be there, intact, when I'm ready to start hiking. Most recently (going to Florida last month), however, I found this to be a bigger cost increase over checked baggage than it has been before (I think I used UPS this time). Maybe because Florida is farther away than most domestic places I've hiked in (?).
I'm going back to Spain in late September to hike the Camino (again) with a couple of friends who are doing it. For that trip I'm tempted to leave the poles home; I used them some on the Camino, but had them in my pack more often than not. I can borrow or buy a cheap knife to cut bread/fruit, etc. And it's possible that an Albergue along the way will have poles left behind by someone else that are free to whoever wants them --- I remember that being the case at least once last time. Would be nice to just do carry-on for an overseas backpacking trip!