While this may be a heavy burden to bear in most countries, in India - a country of over one billion people - it is many, many times greater.
Bindra himself would be the happiest Indian of all, to finally have someone else join him 'in the club'.
Now, Sindhu - on the back of her first world title triumph - has 25-year-old Bajrang to share the weight of expectation in Japan.
Bajrang was born in the Haryana district of northern India.
He started wrestling at the age of seven and it wasn't long before his talent was recognised.
Bajrang's father Balwaan - a former wrestler himself - would travel by bicycle instead of bus, in order to save money and provide his son with the proper nutrition he never had.
The sacrifice paid dividends.
Bronze at 60kg in the 2013 Asian Championships in New Delhi was backed up the following year by silver medals at the Commonwealth Games and the Asian Games at 61kg.
In 2015, the family relocated to Sonepat so that Bajrang could train at the regional centre of the Indian Sports Authority in the hope of perhaps emulating Sushil Kumar in becoming a world champion.
The heir to Yogeshwar Dutt
One of the key figures in Bajrang's rise to the top is Yogeshwar Dutt.
The pair met at a training camp in Delhi when Bajrang was just 14, and Dutt was yet to win an Olympic medal.
Dutt became his mentor, and instilled the values of respect and discipline in his trainee.
Nowhere was this more obvious than in Bajrang's decision not to go to the Rio 2016 Olympics, despite his growing status in wrestling.
Instead, the grappling prodigy chose to support Dutt in what would be his last Games, and not provide extra competition in the 65kg category.
Dutt, who had won bronze at London 2012 at 60kg, went out in the first round in Rio before reciprocating his protegé's respectful gesture by retiring to focus on the younger man's career.
And one of Bajrang's great motivations is to achieve what his guru could not.
"Yogi bhai (Dutt) has played a crucial role in my wrestling career," Bajrang told Business-Standard.
"I am a wrestler because of Yogeshwar bhai. I want to realise his dream of winning Olympic gold and I am working on that."
"It was in 2008 that Yogi bhai (Dutt) advised me to stay away from my mobile phone as it’s a distraction," Bajrang revealed to the Economic Times.
"And I’ve followed his instructions for almost a decade. When he retired from wrestling in 2017, I asked his permission to get a phone so that I could stay in touch with him." - Punia on his mentor Dutt.
Bajrang decided to take the practice a step further, and refrains from going to the cinema too.
“I want to win a medal at the 2020 Tokyo Olympics and I want to keep all distractions away.
"I never think that I am the best or special. I treat every bout as my final bout," he revealed to the Times of India.
"I never underestimate my opponent, whoever he is. I watch videos of my opponent before a bout, whether it is the first round of final, then devise a match-specific strategy along with my coach."
The secret to Punia's style
Another Dutt masterstroke was to employ Russian and English teachers for his pupil.
This international tutelage, combined with training camps in wrestling hotbeds like Russia and Georgia, meant Bajrang was exposed to all styles, and even incorporated some of their moves into his repertoire.
"That was done so that we could understand what the rival coaches and wrestlers are planning during the bout," he told Business-Standard.
"Most of the prominent wrestlers are from the Russian belt, so learning Russian comes handy.
"I mostly use Irani style. It is my favourite as I won quite a few matches using this technique. I keep learning from everyone, be it the coach or a wrestler. If a wrestler uses some different technique which I don't know, I try to learn that technique as well." - Bajrang Punia
Another key factor in Punia's development was the creation of the Pro Wrestling League in 2015.
This United World Wrestling-sanctioned venture brought the world's best to India, with the wrestlers auctioned off to six franchises before competing against one another.
Reaching the top
Bajrang has since taken his consistency and domination to a new level.
Victory at the 2017 Asian Championships and 2018 Asian Games in Jakarta was followed by the 2018 Commonwealth title on Australia's Gold Coast.
In 2019, the Haryana grappler won the Asian Championships in Xi'an, China, as well as at the prestigious United World Wrestling Dan Kolov and Ali Aliev events.
This rich vein of form led to him being awarded the World No.1 ranking for the 2019 World Wrestling Championships in Nur-Sultan.
But he went out in the semi-finals in Kazakhstan with a four-point move by home favourite Daulet Niyazbekov proving decisive as the pair finished 9-9.
Dutt was angry at some of the umpiring, but his charge bounced back to win his bronze-medal match against Mongolia's Tulga Tumur Ochir 8-7.
And Bajrang tweeted, "Sometimes defeat teaches you something you may never learn from winning.
"I will not consider this bronze medal as a victory, but I will use it as inspiration for upcoming challenges."
The Millennial chink in Punia's armour
Bajrang's bubble has been burst just twice in the past three years.
The first time, highly-rated Japanese youngster Takuto Otoguro beat him in the 2018 World Wrestling Championships final.
The 20-year-old ruthlessly attacked the Indian, dictating the tempo of the contest to secure a 16-10 victory in Budapest.
A rematch between these two on Otoguro's home turf at the Tokyo 2020 Olympics would be a blockbuster sellout, followed by millions across Japan and India.
The next loss came at New York’s Madison Square Garden in the ‘Grapple at the Garden - Beat the Streets’ event.
Yianni Diakomihalis of the USA, also 20, used Bajrang's more aggressive style against him, regularly taking the more experienced Indian to the floor to win 10-8.
Wrestling union with Sangeeta Phogat?
Bajrang is undoubtedly the poster boy of Indian wrestling, and he is rumoured to be marrying into the most famous wrestling family in the country.
According to a Times of India report from August 2019, Punia and Sangeeta Phogat will wed after the Tokyo 2020 Olympics.
Sangeeta Phogat is the daughter of Mahavir Phogat, a former amateur wrestler and senior Olympic coach, on whom the Bollywood thriller Dangal is based.
The senior Phogat is also his four daughters' wrestling coach, including Sangeeta and her sisters Geeta, Babita and Ritu.
He also coaches their cousin Vinesh Phogat who won bronze in Nur-Sultan and is also considered a top Olympic medal prospect.
Bajrang and Phogat have remained very quiet on the marriage rumours, no doubt so that they can focus on the Olympics.
A bright future
At 25 years old and with plenty of international titles already to his name, Bajrang has the chance to challenge for global titles for years to come.
His unrelenting work ethic and deep respect for opponents have contributed in making him a household name in India.
Now all he needs is to do is leave it all on the mat in Japan next year.
If he is able to cope with shouldering the hopes of a billion Indians, Bindra may soon have company in India's Olympic gold medal club.