Donald Trump is a gift to caricaturists – and not just because of his unreal yellow quiff and angry orange face. He is a satirist’s dream because he reacts. The poor man has not got it in him to ignore a jibe. When protesters floated a big baby Trump blimp for his British visit last summer, he said it made him “feel unwelcome”. So like foxhounds scenting blood, his tormentors have relaunched the inflatable for his state visit. The Museum of London wants to put it on display. It is well on its way to becoming a national treasure.

So we will probably see this mildly funny balloon many more times. I could hear someone on video, as the nappy-wearing blimp was launched from a glum grey Parliament Square, lecturing reporters on its place in the history of British satire. So is this really a masterpiece of protest art – or does it pop when you take a sharper look?

As a caricature of Trump, it ticks all the boxes. Absurd crown of fake-news hair? Check. Open snarling mouth? Got it. Angry eyes glaring through narrow slits? Done. Brass complexion? Full marks. Yet the blimp’s creators haven’t really done anything imaginative with Trump’s features. This is hardly in the imaginative league of Honoré Daumier portraying the French King Louis-Philippe as a pear; or Gerald Scarfe exaggerating Margaret Thatcher’s features to give her a vicious beak; or Steve Bell turning David Cameron’s head into a condom. The creators of Baby Trump have kept it simple, however, because they don’t need to do much. Trump comes pre-packaged for laughs. All the caricaturist has to do is accurately capture his trademark features: the straighter the portrait, the more impossible it looks.

Monstrous joke … the blimp is inflated in Parliament Square. Photograph: Matt Dunham/AP

Has there ever been a political figure whose own cultivated brand was so guaranteed to strike many people as a monstrous joke? English satirical artists 200 years ago excelled at reducing politicians to an extreme shorthand of themselves. James Gillray always drew the Tory war leader Willam Pitt the Younger as a skeletal stick and his Whig enemy Charles James Fox as an unshaven shifty criminal. It seems unlikely they looked anything like their caricatures – although there are no photos to compare. But if Trump stood next to his blimp they would appear to be brothers.

So the blimp is not so much revealing of something we didn’t see before as showing us what we already knew. It invites a snigger of recognition. The trouble is that Trump made himself into a walking grotesque for a reason. He wants to be noticed and remembered. He’s a fool to whinge about the blimp because all it really does is advertise his brand. Donald, think about it! A blimp selling your face and it doesn’t cost ya nuthin’! Since Trump won a presidential election having already been exposed as a bully, liar and worse, he is arguably beyond being mocked. Satire can hurt his feelings, but not necessarily damage him.

More protest art … Ollie Nancarrow mowed a penis into a field as a message to Trump as he flew in. Photograph: born-eco.com

So what this work of political art actually does is make us feel we have more power than we do. Britons can’t get rid of this lamentable president. Instead, we can insult him with rude art. The Trump blimp has been joined this week by other deliberately offensive artworks. A student mowed a giant penis into a meadow under the president’s flight path. A statue of him sitting on a gold toilet has been erected in Trafalgar Square.

The blimp’s big insult, its thrown shoe, is to depict Trump as a baby holding a mobile phone. This is its one insightful twist. Trump truly is like a big baby – an unruly, instinctive being who wants and wants; a living parody of American individualism. Great American novelists have explored the wilful individualism of the American man but Trump reduces it to nappy-filling infantilism. From fast food to models, he wants, he grabs. He is a walking travesty of the American right to the pursuit of happiness: a more mordant living artwork than any inflatable can match.

So why not take it further. If Gillray was alive, he’d be so much more vicious. A nappy? He’d have shown Trump’s rump unpresidentially bespattered. This blimp reassures Trump’s British critics by empowering us through easy laughter. Sadly, it is not great satirical art.