So ends a good week for Britain's republicans. You might imagine that the birth of a future king to a popular and engaging royal couple would be a catastrophe for the anti-monarchists, but not a bit of it apparently. According to the pressure group Republic, which pushes for a democratic alternative to the Windsors, it has been swamped with thousands of membership requests, plus unprecedented interest on social media.

"It's a myth that big royal events are bad for republicans," says Graham Smith, chief executive of Republic. "Quite the opposite. These events – the wedding, the jubilee – are blown out of proportion by the media and the way they portray them doesn't reflect public opinion or attitudes. Most people are looking at the coverage of the birth and wondering what the fuss is about. They want it stopped."

If statistics are to be trusted, a quarter of readers will agree with Smith. Another quarter will spit out their breakfast in apoplectic protest. But about 50% of Britons do not feel strongly either way. Republic estimates that there are between 10 million and 12 million republicans in Britain – its 10,000 Twitter followers suggest that's optimistic – but, whatever the figures, individuals espousing those beliefs were thin on the ground last week.

For one day, the Sun became the Son. Another paper devoted 21 gushing pages to the unnamed "royal baby" on Tuesday and then went on to describe the BBC's coverage as over the top. On BBC Breakfast, the birth was hailed as a triumph for "Brand Britain". Reporters Nicholas Witchell and Kay Burley were ubiquitous. Even the Guardian claimed record traffic for its live blog of events surrounding the birth.

It would be inaccurate, too, to portray the birth as merely a parochial concern. The front page of France's Le Matin splashed with "C'est Un Garçon!" and most of the world's media gave the news prominent billing, including heavyweights such as the New York Times, which called it "a spectacle unlike any other in the modern media age". One poll showed there was greater fascination in the baby in India than in the UK. Now the hysteria has dissipated and TV crews from around the world have gone, it is an appropriate moment to take stock. Has the arrival of Prince George told us anything we did not know before about our attitude to the monarchy, class or giving birth? Beyond that, have we learned anything about Britain's status in the world in 2013?

"We've got a situation now where the British royal family are becoming the global royal family," argues Tristram Hunt, historian and Labour MP for Stoke-on-Trent Central. "They have achieved a breakthrough status much more than the Spanish royal family or the Dutch or the Japanese royal families. That's partly because of Diana and it's partly the way in which the world views Britain now. The royal family is a signifier of history and heritage and a vision of Britain. They have achieved a global celebrity status."

Is that a good thing? "Of course, the royal family is very traditional, but the image is of a young, photogenic, happy, modern, comfortable-looking young couple," Hunt says. "He's dressed in Boden, she'd dressed in God knows what. It doesn't seem to be a bad image for the country."

Smith from Republic begs to differ. "It's done us harm in terms of our reputation in the world, because it doesn't reflect Britain as we are," he says. "The problem when you talk to people overseas is that quite often they think we are this tradition-obsessed country that loves the royals and is all very quaint and the rest of it. In fact, we're an incredibly modern, vibrant and exciting country with an innovative and entrepreneurial economy. That's completely lost in these events – it's really unfortunate."

One aspect everyone should agree on is the so-called "baby bounce" that will lift the country's stagnant economy. Except there's no consensus here either. The Centre for Retail Research was confident to put an exact figure on the retail benefits: £243m. This was broken down into £80m on souvenirs, £76m on books and DVDs and £87m on the rather nebulous category "festivities". The centre estimated that 3m bottles of champagne and sparkling wine would be opened. These sums have proved easy to poke holes in. Hunt is bullish about the ceramics orders coming into the Potteries, but much of the memorabilia will be made outside these shores. The champagne corks will benefit the French economy more than the British. A YouGov poll of 1,577 British adults, conducted before Prince George's birth, found that only 1% of respondents would be "very likely" to buy commemorative merchandise, while 89% were "totally unlikely".

Even if we do not challenge the £243m figure, the Financial Times showed that this equated to a GDP rise in goods and services of 0.06% in a quarter, an upturn it derided as "puny".

By the end of last week, with William, Kate and George ensconced at the inlaws' in Bucklebury, Berkshire, it was business as usual at the landmarks of the royal birth. Outside the Lindo wing of St Mary's Hospital in Paddington, west London, the Burt family from Portsmouth posed for pictures. "We expected more people, certainly around here," said mother Sarah Burt. "We've just come from Buckingham Palace and we thought we would swing by before going home."

What was it that the family liked about the Duke and Duchess of Cambridge? "They just seem like a very genuine couple," said Sarah Burt. "It's a love story, isn't it?"

At Buckingham Palace, a mother-daughter pair, Geertje Hans and Marit Swart from Harderwijk, in the Netherlands, seemed a little bemused when asked if the Windsors were now the world's royal family. "But we have our own," replied Hans. She did, however, recognise that there was something distinct about the British monarchy. "Ours are closer to the people and here it is more formal. At home if you saw Queen Beatrix in the street you would just shake her hand. They are not special people. I can't imagine that I would shake Prince Charles's hand."

Of course, for many British people and outsiders too, it is the fact that the royal family are untouchable that lends them their great allure. In an age of reality-television celebrities, they present a refined, eternal and anachronistic alternative. The addition to the lineup of Kate Middleton, a "commoner" as we are often reminded, has brought an intriguing dynamic. She is perfect, but not threateningly so; even shortly after coming through labour, she addressed the press with immaculately blow-dried hair cascading into tousles.

It is in keeping with the enigmatic profile of the royal family – and its public-relations advisers – that we still know almost nothing of interest or importance about George's birth. Even with the hours of TV coverage and the endless pages of newspaper analysis, details are scant. That is partly why the media mainlined on fripperies. We were told, for example, that Middleton wore a Jenny Packham design on the first day and a Seraphine lavender wrap dress with Givenchy sunglasseson the next. George was swaddled initially in a £12 aden + anais wrap, before changing into a £45 GH Hurt and Son christening shawl.

The desperation for a new angle led to some misguided decisions. OK! magazine was threatened with a boycott – and forced to issue a grovelling apology – after its cover promised to share "Kate's post-baby weight loss regime". Printed before Middleton gave birth, it speculated, "She's super-fit – her stomach will shrink straight back."

"I read the headline and it was literally like someone had smacked me in the face," says Katy Hill, a TV presenter whose tweet started the backlash. "Headlines like that do affect people: no new mum should have her euphoric baby bubble burst because she thinks, 'I better lose my baby belly'. That's really morally wrong."

Surely most of us, whatever we think of the baby, believe it is time to move on. The only group with a vested interest in the saga continuing are the republicans. "I'm not saying we are on the cusp of a revolution," notes Smith from Republic, "but the movement is in the best health it's been in since the era of universal suffrage."