I did the Southern Tier from San Diego to Pensacola on a road bike. The 1990-ish Cannondale Criterium road bike and worked out well IMO. I much preferred it to my touring bike for lighter touring. The tires I started with were somewhat worn 23 mm gatorskins and I switched to 25 mm gatorskins when they wore out completely. The buzz on the Texas chip seal was pretty bad with the 23 mm tires, but much improved with the 25 mm ones. I weighed maybe 205 and was carrying a base gear weight of about 14 pounds at the start and a bit less at the end. That included full camping and cooking capability.

I used a triple converted to a double by leaving off the big ring. Gearing was 39/26 front and 12-28 rear (7 speed). That worked out well for me. I did have 32 spoke wheels though.

I rode with a guy on a carbon road bike some of the time on that tour and he used a BoB trailer, and carried a heavy load, but did have mechanical problems that he blamed on the trailer. His problems were related to bent derailleur hangers and subsequent wheel damage. I am not convinced the trailer was at fault, but maybe it was.

I see no reason why you couldn't do fine with a modern road race bike if you travel light and maybe even if you don't. Without a trailer I'd be leery of low spoke count wheels unless you and your gear are fairly light. A lot of this is personal preference though.