CSX and Norfolk Southern have the ability to deliver containers to Chicago, which is the main interchange point between eastern and western railroads. Granted, rail cars can get lost in the bowels of Chicago's rail yards for some time, but that can be fixed.
Interstates 10 and 95 can get containers moving onto our highway system with ease.
A little imagination and willingness can get things moving to the right places.
I think Jacksonville is the southernmost Florida port served by NS. Anything south of there is going to ride on either CSX or FEC.
BN and UP serve Gulf ports as far east as New Orleans. KCS (soon to be part of CP, if it isn't already) goes to Mobile. CN gets to Mobile as well on the old IC-GMO lines.
The Florida ports aren't major container ports. New York, Virginia, Charleston and Savannah are the big Atlantic container ports. Brunswick appears to be mainly RoRo, with Jacksoville and Baltimore being big RoRo players. Top 10 list for containers here: https://container-news.com/top-10-the-busiest-container-ports-in-the-united-states/
CSX and Norfolk Southern have the ability to deliver containers to Chicago
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Ability yes ; adequate number of people to unload the containers, no ; adequate number of truckers to truck them away, no ; adequate number of warehouse workers to unload the trucks, no.