It's a rather complex issue, this is a great recent article from people who study bananas (as opposed to pop-media journalism):
The trap of extinction stories on bananas : Under the peel | Information and news on bananas from ProMusa
I mostly agree with Nick's answers, except Gros Michel vs. Cavendish yield. It might be true for some clones under certain conditions, but it's really never been a driver of choosing Cavendish over Gros Michel, they are very closely related and relatively equal under good conditions. If Panama Wilt is not an issue, dwarf Gros Michel cultivars are highly desirable and generally more desirable than Cavendish cultivars, and they both get Sigatoka diseases easily. Gros Michel is still grown in large quantities around the world, just not usually for export).
There are some exported to the US and Europe still, just in small amounts and are very speciality.
Basically it comes down to the issue of Panama Wilt Race 1, which is not just in Latin America, but is present almost everywhere bananas are grown to some degree. There are ways to control it and keep plantations relatively clean, but they are costly and can be difficult to implement with the pre-established systems. Any banana cultivar can be grown and exported with enough tinkering of the system, but only very few can come out of that system and still cost under 70 cents/pound at your local grocer and would be able to compete directly with Cavendish. A good example is Manzano (Silk), which is relatively common in US markets, but they are much more expensive than the Cavendish bananas they are typically displayed next to, so end up being more of a novelty experience than an everyday kind of banana.
To grow Gros Michel in large enough quantity to make export feasible in the normal Cavendish-based market requires very large farms, which are then easy to let Panama Wilt get out of hand on. On small, diversified farms, it is not as big of an issue, so Gros Michel are still very common in local markets in the tropics.
Also just to be nit-picky banana nerd; bananas do not require pollination of any kind to set fruit, they are vegetatively parthenocarpic.
All the talk of Panama Wilt really out shines another potential serious headache, which is Banana bunchy top virus (BBTV). It is not present in the Americas at all at this point, and is somewhat more difficult to accidentally introduce compared to Panama Wilt strains, but if that is ever introduced and became established it would very quickly put Panama Wilt Race 4 on the back-burner for export Cavendish problems in Latin America. It turns out Gros Michel cultivars are actually somewhat tolerant to BBTV.