I would rent from Kingdom strollers or similar. A few years ago I had just bought a stroller worth over $1000. Gate checked it on our way to Orlando and when we got to Orlando my mangled damaged mess of a stroller was waiting for me on the ramp. We were informed that damage is not covered by the airline, only loss. SInce it was totally brand new and purchased online with a VISA, VISA had a seperate insurance and they reimbursed me for the stroller once we got home and looked into it all. An online search for what to do when the airline ruins your stroller, btw, had plenty plenty plenty of stories of people that experience the same thing as I did....its pretty common. From then on we rent. Its a pretty minor expense in the overall scheme of the vacation and its worry free hassle free for us. With 8 kids we even rent 2 strollers, doubles, and its still worth it over bringing ours. Arriving at Disney without a working stroller was a panic moment. The first day we had to make due with the one until we could get a rental delivered....and we have just rented every since.
The downside of those convenient little umbrella types is they are horrible to push, never the right height, have a weird stride length to them so you are always hitting your feet on it, are not very comfortable especially for napping if they even recline at all, have little storage etc. We don't go back to the room for naps and little ones nap in stroller so those things are important to us. Plus with 8 kids you just have a lot to haul in and out of parks...we need storage space! The walk from gates to magical express is short enough for us that we don't need a stroller at the airport. I bring 2 baby carrier packs (Ergos) and wear the smallest one on front one on back and the rest are perfectly capable of walking that small distance. Especially after being on an airplane for hours, heading to sit, again, on a bus, when they are pumped for Disney!