If it weren't for Senku, most of the other human characters in Dr. Stone would be completely lost. None of the petrified humans would have ever been revived. The humans in the Ishigami Village might have remained stuck in the stone age for another 3,700 years. Senku's encyclopedic knowledge of all things science not only makes him the most qualified person to rebuild society, but he uses it to solve many more immediate problems. For all of the times that science is used to resolve issues in this series, the characters who aren't scientists risk coming off as nearly useless.
However, just because not everybody knows everything about science doesn't mean that they're useless. Each character has something they can do to help rebuild civilization. Senku's role just happens to be the most important and pronounced.
What makes it especially hard on the rest of the cast is that the story is designed so that science is the only thing that can save the day. A major aspect of Dr. Stone is showing off various scientific discoveries and inventions and their practical applications. Thus, nearly every conflict or obstacle is overcome with the latest discovery or invention. Unfortunately, this need for Senku's latest scientific achievement to resolve an issue leads to any other solution being rendered useless. This is arguably why Kohaku, despite being one of the Stone World's greatest warriors, never gets to win an important fight. It's also why the Ishigami Village never made any technological progress despite having a 3,700-year lead on Senku; they instead dismissed science as some kind of sorcery. Naturally, Senku has to rely on science to resolve conflicts like these, but it comes at the cost of making everyone else seem helpless by comparison.
With all that said, Senku can be pretty helpless when he's by himself. For the first six months following his revival, he stuck to basic stone and wooden tools to get him through his daily life. At this point, he was no better off than anyone in Ishigami Village. Senku's biggest problem is that he's physically weak. He knows everything he needs to know to rebuild society, but he doesn't have the strength to make any of it happen. To put it in video game terms, like the character in question, it's as if he dumped all his stat boosts into intelligence, so his other stats are still at the base level. All the knowledge in the world is useless without the power to use it all.
It was only when Senku either made or revived allies in the Stone World that he was able to start making any real progress. With their help, Senku had the smarts and the strength to gather materials and make things out of them. Of course, this doesn't mean Senku won't pitch in when necessary. What's important is that he's there to coordinate the rest of the cast and work with them to build what needs to be built.
Besides manual labor, Senku gets a lot of use out of the other characters through their respective fields of expertise. Kaseki's craftsmanship was necessary for putting together some of the more complex inventions of the series, especially those made out of glass. Yuzuriha, who's also good at crafting, proved herself useful through clothesmaking and, more importantly, reconstructing the destroyed stone statues. Gen's mentalist abilities have helped him talk the Kingdom of Science out of some pretty sticky situations. In later seasons, Ryusui will be depended upon for his sailing and navigation expertise. Everybody brings a skill to the table that Senku doesn't have.
Even if the others aren't scientists themselves, they can still put forth some good, helpful ideas. When Senku was developing his revival fluid, Taiju proposed that he use grapes as a source of alcohol. Chrome took the lessons Senku taught him to recreate things like the water wheel and sodium hypochlorite; this is especially impressive considering how, unlike Senku and the other revived humans, he had no prior knowledge of these things. These amateur scientists provide a fresh perspective on certain problems and find solutions that Senku couldn't come up with by himself.
The only characters who still get a raw deal in the Kingdom of Science are the warriors. Again, since the story necessitates that all problems be solved through science, they'll almost never be allowed to win a major battle. When it comes to science work, their power is generally just used for manual labor that the others can't handle. If were any other Shōnen Jump manga, this power dynamic would be completely reversed.
The non-scientists in the kingdom of science also serve the narrative purpose of representing the average person's knowledge and intelligence. Senku has a nasty habit of explaining the science behind things in ways that can make listeners feel stupid for not knowing what he's talking about. The rest of the cast's responses to what he has to say let the audience know that if they're feeling lost, they shouldn't feel alone. This especially applies to the revived humans who lived with modern technology but only have a passing knowledge of it at best; Gen's reactions, for example, are about what the writers expect the average person to respond to Senku's words. The audience is presumed to know a little about science from one source or another, but no nitty gritty things like complex chemical compounds or the inner workings of a phone.
Senku may be the smartest man alive, but he needs everybody else just as much as they need him. While he provides the science, they all provide the manual labor and other essential skills to make his visions a reality. It's a synergistic union o mind and body that requires the cooperation of everybody in the Stone World. Without any one of these talented people, Senku's plans for rebuilding humanity would have either never happened or would have at least been set back by many years. He needs them just as much as they need him.