I absolutely don't agree about only 1 or 2 agencies for teaching. First, there are caves outside of Florida. Second there was or still is an agency nacd called that found also his basics in Florida, did they do bad work in the past before the problems started? Ok, now more serious, you see that a lot of Mexican divers think they invented cave diving, the same with divers from Florida and the same with divers from France.
If you look back in the history of cavediving, you see that things started parallel, so there was exploring in Florida, there was also exploring in Europe and there was exploring in Mexico. But all did it their own way because the caves are also different. The overhead and water are the same, but the rest can be different. Later things came together, but some things never will come together. For example the sump diving in the UK or France. If you have been only in Florida, you will absolutely have no idea about what this kind of diving is. If you only dove in Mexico, you will never have felt the strong currents in Florida. If you have only been diving in Europe, you will never have seen really complex caves (but complex mines yes). We have one more or less complex cave in the south of France, Font Estramar, but diving is officially forbidden there sadly. I have been there when it was not closed. But most other caves here are quite easy with 'complex' navigation.
But what about mines? Europe has quite a lot of mines. And they can be very complex (deep, cold, lot of sidetunnels).
I think teaching has nothing to do with the agency. But it would not be a bad idea to put in standards that divers have been in different regions and caves before doing an instructor course. But this can also be in Europe only for example. We have more than only the Lot region in France with caves. We have mines, we have the Jura, the Doubs, Spain, Italy, etc. I learned cavediving in Thailand. The caves I dove in were dry caves before 1982. Then they flooded them on purpose. So the complete structure was known before they were under water. I dove in Europe in caves and mines.
I did one of my cave instructor courses in Europe. And for my ccr cave instructor course I went to Florida. I did it with Tom Mount, also not an unknown person in cave diving. I am a diver who went from twinset to ccr to sidemount and now also do some sumpdiving with sometimes climbing.
But there are also cave divers and cave instructors who came from speleology and then moved into sumpdiving and now teach cave diving to only divers. That is a different approach and does not fit in a lot of agencies.
Also things that work in France and do not harm the environment will harm in Mexico. Steel sidemounts vs ali sidemounts. What is better? In Europe you also see steel tanks for sidemount or bailout with floats on it to compensate the negative cylinders. Is that wrong? That is never seen in GUE, but it is not wrong.
Is it wrong to do a cave course directly in ccr or sidemount? Not all agencies allow this, but I think it is not wrong.
And also nss cds and gue teach trimix/ccr/sidemount. So they also teach all.
I think 1 thing that has improved in the last 10 years is that there is more knowledge easy available due to internet. Divers can discuss things and divers sometimes are more open to mistakes they made in the past.
And remember, there are no statistics that 1 agency has more accidents than another agency. As all divers have to deal with the same physics, and water can kill all over the world, there is no worst or best. The discussion to improve things is always good and is not agency dependent.
And diving can be dangerous, like riding a horse or driving a car, so accidents will happen. We can discuss how to avoid stupid accidents, but it will be impossible to avoid all accidents. Divers are still humans.
About panic:
Panic can always happen, also the instructor is human and can get into panic. Some people are more prone to panic than others. But getting experience lowers the risk of panic. That means you still need to train or improve yourself, even if you have already a lot of experience.