I think that if you used flour alone as a binder it will just make them sticky and glue-like in texture once heated.
The reason for that flour does this and cracker crumbs or bread crumbs don't is that the starch granules in raw flour and in crackers and bread are in different forms.
In the presence of water (and heat, which speeds the process up), starch granules absorb the liquid and burst, creating a gel-like substance. If you have ever made a sauce thickened with flour (or a simple flour glue/paste for children), then you have seen this in action. When making bread and crackers, the water content is low enough that the burst doesn't fully happen, and the starch interacts with the gluten in the flour to form a solid network. Both of these processes are non-reversible, which is why your bread and crackers don't dissolve into a gloop if you mix them into water or dip them in your soup.
I think (not having done this) that if you used the crab and bound with flour, at least in the central parts of the cake, the moisture driven out of the crab during cooking would be enough to gel the flour, whereas the breadcrumbs/crackers will retain their texture and produce the nice fluffy cake.
Edited to add: This has reached the "hot network questions" so a disclaimer here: This answer is my untested theory; one commenter (@chipbuster) tested with meatballs and found no gloop using an air-fryer. You also don't get gloop making things like fritters; which are made with flour and usually cooked similarly to crab cakes, though they are flatter, so heating is quicker... Feel free to test and comment and/or edit with your findings - or upvote @ChrisH 's answer if that is the right one.