I bought two bicycles in Italy during extended trips there (30+ years ago). The first one came back whole. I brought the second one back in pieces over 2 trips.
I rented some cruisers in Egypt for a day trip. That was fun.
I haven't considered rental/leasing for other trips. I did pick up a used Bike Friday Pocket Rocket which I've used off and on. It can be handy to stuff it in a suitcase, and if you an keep your baggage under control, you should get the Pocket Rocket shipped without any special fees.