What are you talking about? 3.7m is the road limit. ULA builds them in Decantur with river access and a custom built vessel. I think I heatd that the current bridges on the river limit maximum diameter to 6m and something. But that's at current factory. Also, the Atlas V core is 3.9m, which is designed to be transportable on an AN-124 (so is the Antares core). And Michoud is open to rent for zones, were you could do 8.4 to 10m depending on construction method.
I know that road limit is 3.9 but you can push it to 5m wide without too much trouble after that you have to start modifying bridges etc.Who ever picked the site for Michoud was a very clever man indeed.
I can't recall exactly what the total height limit is, but I guess it's close to 4.2m. But that's the top dynamic height for the whole transport. Once you take into consideration the support structure, the environmental protection, the clearance to the road plus the possible vertical curvature of the road and all such you arrive to an effective maximum height for your delicate cargo of around 3.7m (plus or minus a bit). You can do wider reasonably easy, but rocket cores are cylinders.
You can go a bit higher if you study the road, but ten you have to get a permit per each state you cross. And if you go higher you have to get a permit per county! Thus, 3.7m is sort of the maximum width that you could transport easily. Let's say that you want to transport a fairing that's 7m wide, but each half is 3.5m, you might do it cheaply. Or just look at the drawing of the Rocketdyne's F-1 transport rig.
Yet, water or even road transport are not always the cheapest way. Say, for example, that you do have a port, but it's on a shallow water way, or is very far from major traffic lanes, then it might cost you more than do a straight airlift. Ditto for very far places. Sometimes train is cheaper.
For some reason LM decided that 3.9m air lifted was better than 3.7m road transported. Now that they are unified on ULA, they ship it by water if they can consolidate it with some extra cargo, but if they only have to ship a single Atlas V core, they still send it by An-124. The US is a great place to move things around, all the logistics are reasonably optimized. Thus, airlift can be cheaper than even road transport for certain cases.
The reason MD/Boeing chose the wider core for Delta IV was because they chose H2 as core fuel. And because they expected to make tens of launches per year. At that rate, having a ship that can transport 3 cores per trip might well be cost effective vis-a-vis even road transport. Currently it's not. But they don't have that option.
Now, let's say that ULA can transport the wide cores and even a 10m fairing, if so they chose (which they can). Never forget that rockets are a mean to transport payloads, not an end in themselves. What there's a total scarcity, is of all the support structure for bigger than 4.6m payloads. Think about transporting those, about anechoic chambers, environmental testing chambers, shakers, clean rooms, etc. I would recommend that you look up videos about the ATV's processing. They clearance above and on the sides when entering a clean room is around 10cm. And all the things I've mentioned are cubically more expensive with scale. Thus, if you have a clean room that could fit a 6m payload, you would have to charge about twice for your services than a 4.6m one. How many clients would you expect?
You are making the point I was making I was complaining about 7.7 m cores.