The problems of transatlantic diffusion theories
The real challenge facing oceanic hyperdiffusionists is not so much that the comparisons of data they build their theories on are necessarily weaker than those made by more orthodox "evolution in situ" scholars. It is that their theories are necessarily more complicated and leave more to explain, thus leaving more to go wrong with their explanations.
The chief problem with positing a West African origin for Olmec culture is that one would expect such kinds of trans-Atlantic travel to leave EITHER more OR fewer traces in Mesoamerica, than the ones we actually find.
Occasional one-way ocean crossings are not hard to believe in during much of prehistory. There are records in early modern times, for instance, of Inuits who survived an accidental kayak trip to West Europe; certainly W. Africans could have wound up in the New World ~1500 B.C.-~500 C.E. But those Inuits did not establish colonies in the Hebrides, and we do not seek the origins of Renaissance realism in Inuit animal carvings.
Any WA fishers or traders who landed in Mesoamerica would have been unlikely to set sail with women, plant or animal domesticates, and toolmaking specialists - the kind of cargo you need in order to transplant your culture onto an alien shore already settled by others. At their luckiest, these stranded sailors would have been adopted by an indigenous tribe, married native women and adapted to native culture. It is most unlikely they would have been elected to local chieftaincies, any more than today's refugees wind up running for president in their lands of refuge.
If they did pull this stunt off, thereby persuading Native American sculptors to render them immortal - then they must have done so by HAVING SOMETHING ON the locals, culturally. Some items of Old World culture would have had to give them an advantage over pre-Olmec Mesoamericans. Well, what items were they? Millet or cattle or bronzemaking? And if they had such items, *where were they in 1492*? Why hadn't they diffused far and wide throughout Native America, the way the Spaniards' horses did, far beyond the writ of the King of Spain?
In modern experience, seafaring cultures that are successful enough to plant colonies on previously occupied shores are usually successful enough to establish regular round-trip voyages. Any fool can set out to sea, after all; the test of seamanship is being able to get back home again, as any sailor will tell you. But the supposition of round-trip travel between Guinea and Mexico creates even more problems --
E.g., why would they have bothered? For what did they trade, that was in short supply in WA and so valuable that it would be worth the incredible hazards of trans-Atlantic travel?
E.g., why didn't they bother to pick up any of those incredibly useful Mesoamerican plant cultigens that had swept across Europe by 100 years after Columbus - as well as Africa and Asia? Or did they really, and WA'ans actually had maize and tobacco and tomatoes all along - but somehow the Euros overlooked them?
E.g., how come they didn't establish "Olmec" way-stations? Nobody in his right mind sails directly from Europe or Africa to the Isthmus of Tehuantepec - you have to go via the Greater Antilles and Florida, as the Spaniards did. And you would found colonies there, as the Spaniards did, leaving plentiful signs of them today. So where is the "WA Olmec phase" of archeology in Florida, Cuba, Hispaniola and Puerto Rico? You can't have it just in Mexico.
E.g., why didn't they transmit Old World diseases to the New World the way Europeans and Africans apparently did in 1500? Epidemics devastated Native Americans from pole to pole, post- Columbus, arguing long isolation from Old World pathogens. If WA'ans had been mucking around in Olmec Country, would not that patch of Mesoamericans at least have experienced these diseases at that time? But in that case, (a) they would have been already present in Mexico by 1500 and (b) they would not have been as lethal as history records they were at that time.
One could go on and on. The problem is not that one can't cobble together an argument that ingeniously links, say, Mandes with Olmecs - or any other hyperdiffusionist pairing - but that in order to make ANY such theory work, one is driven to add so many bells and whistles and other moving parts that it becomes increasingly cumbersome and unlikely.
Oceanic diffusion theories are the scientific equivalent of Jaguars: man, they look sexy and they're sure a lot of fun to drive, but they're constantly breaking down. Scientists prefer indigenous evolution theories (at least to go to work in) because they're more like Hondas: simple and easily maintainable. *That* kind of elegance.
So it does not require a "conspiracy" or "blindness" on the part of orthodox thinkers to turn up their noses at glamorous diffusion propositions. Diffusion seems to explain one comparison neatly, but usually at the cost of making six other explanations more complex. There is an extra burden of proof to make the complex theories work BETTER than the simpler explanation of chance convergence.