Indeed, "Vulcan" was the proposed name for a hypothetical planet that was suspected to exist within Mercury's orbit (it was thought to be the reason for Mercurian orbital anomalies that were eventually explained by General Relativity). The planet was proposed in 1840 and wasn't disproven until 1915, so the idea was part of the culture for some time and continued to be remembered even after 1915. Various SF authors used the cis-Mercurian Vulcan in stories in the 1930s and after. So it was around in the popular culture as a name for an alien planet during Roddenberry's youth. (And Doctor Who independently had a planet Vulcan in a 1966 episode, after ST premiered but before England would've seen it.)
There's no need to postulate any "fixation" on Roddenberry's part. Anyone who grew up in Western culture, and received the kind of classical education that's apparently less common today than it was in his generation or mine, would have been steeped in Roman cultural references. For centuries, Western civilization has fancied itself the descendant of the great Greek and Roman civilizations of antiquity, and pretty much all of Western civilization is loaded with allusions to Greece and Rome. Any "fixation" is society-wide.
Also, Roddenberry didn't create the Romulans. Paul Schneider did. Apollo was created by Gilbert Ralston and Gene Coon. The Platonians were created by Meyer Dolinsky, after Roddenberry had stepped back from the showrunner role. It's a huge mistake to assume everything in ST was created by Roddenberry personally. He liked to give that impression after the fact, but in reality his greatest contribution was in gathering together a group of talented people who had good ideas of their own.
Same with TNG. We don't know if Roddenberry himself came up with Deanna Troi's name. He got sole creator credit for TNG, but in reality it was a joint creation with David Gerrold, Bob Justman, and D.C. Fontana.
As for the Roman planet in "Bread and Circuses," yes, GR did co-write that one, but as with all their "Earth-parallel" episodes, it was written to take advantage of leftover props, costumes, and set pieces from earlier historical movies and shows. It doesn't show any "fixation" beyond a smart TV producer's determination to save money.
Besides, if Roddenberry had had some kind of abnormal "fixation" on Ancient Rome, wouldn't it logically follow that the TV series he created would've been about Ancient Rome?? Instead, the first show he created was about a present-day Marine Corps lieutenant on a stateside base in peacetime; the second was a cop show (which never went past the pilot); and all the rest were science fiction or supernatural mystery. That sure doesn't seem like a Roman fixation to me. It seems like the career of a TV producer who started out writing what he knew (military and police), then tried out a different genre (SF), and then stuck with that genre for the rest of his career because it was the one that had brought him the most success.
Also, the Greeks and Romans were cultures of huge influence on the course of human development. It's only natural to be attracted to the theme, depicting a similar kind of culture on other worlds.
