You’ll have seen, reproduced in print or online, The Singing Butler, Jack Vettriano’s painting of a posh couple dancing on the beach, sheltered by umbrella-carrying servants. You might also have seen Coal Drops Yard, the shopping centre in King’s Cross, London, that is surmounted by a pair of “kissing” roofs. The latter, in its fusion of romance and rain exclusion, could be considered an architectural realisation of the former.

The designer of the kissing roofs is Thomas Heatherwick, who is to architecture what Vettriano is to art (or EL James is to literature, or Katherine Jenkins is to music), that is to say, someone whose success and popularity is matched by deep critical scepticism. I’d put Bjarke Ingels in the same company – the Danish-born, New York-based impresario who designed a Lego-like headquarters for Lego and makes apartment complexes look like mountain ranges. His tone is more knowing and ironic than the wide-eyed wonder that Heatherwick presents to the public, but his main move is to say: this is spectacular, this is blatant, this is memorable, and why not?

This spring, each is unveiling their most striking landmark to date. In April, in Copenhagen, the long-awaited Amager Bakke waste-to-energy power plant is due to open, designed by Ingels and his practice BIG. It is a structure that combines an environmentally conscious public facility with a ski park descending its sloping form. Hey, it says, you can be good to the planet and have a laugh. Function follows fun. In New York, meanwhile, Heatherwick’s Vessel, the 150ft-high “public sculpture” composed of multiple staircases, offers the public a different way to clamber over the city. Like the power plant, it promises childish pleasure – city as playground, art as climbing frame.

Which is similar to the appeal of Vettriano, Jenkins and James. They speak directly to the simple emotions, say their fans, and bypass the usual gatekeepers of taste and value. It helps, goes the narrative, if you are self-taught and, therefore, spared the obfuscation and doubt that is inculcated by academies. This is true of Vettriano and James. It’s also a big part of the Heatherwick story that he studied design rather than architecture. This background liberates his vision, or makes him inept in basic questions of scale and use, depending on your point of view.

Ski slope on Bjarke Ingels’s Amager Bakke power plant in Copenhagen. Photograph: Rasmus Hjortshoj

For it’s true that education complicates things. Architects (usually – it depends where they study) get taught to worry about such issues as a building’s context, the relationship of detail to the whole, or of appearance to structure and function. They are generally taught to mistrust their first concept for a project, to test it against multiple considerations. If a student is told that their design is a “one-liner” – that it’s only got a single idea – that’s not a good thing.

Ingels and Heatherwick blitz these scruples. They offer at most two-liners (it’s a power plant and a ski slope, it’s a garden and a bridge). Part of their shtick is their apparent facility, the appealing myth of the napkin sketch that turns into a building. Ingels doesn’t seem too troubled about the elegance of his details. Heatherwick has the magical ability to make budget constraints, which architects are also taught to respect, vanish. He is able to attract the sort of client with the means to pay no matter what to build a slice of his genius. One such is Google, who has hired both Ingels and Heatherwick to design HQs in Silicon Valley and London. This overload of ego and vision might seem like a pudding overegged or a lily gilded but it’s the kind of thing you can do if you’re Google.

Well, I’m one of those sceptical critics. I love the idea of the ski slope/power station but need to be convinced by how it works out in reality. Vessel seems to be offensively indifferent to the buildings and spaces around it; I wonder how great it will really be to go up and down its stairs. I like things such as nuance, complexity, multiplicity and depth, in architecture as in other art forms. It seems obvious and fundamental to me that cities are made of multiple buildings playing off each other, not by autonomous objects.

I also oppose a culture that invests little in the dignity and beauty of everyday places – streets, schools – but finds billions in its back pocket for corporate spectacle. But those more reflective architects, and the critics who support them, have to recognise that Heatherwick and Ingels present a challenge. There’s real power and attraction in those excessive constructions. They appeal to a desire that people have of their surroundings, to engage and excite them. The really impressive achievement would be to respond to that desire with structures that have more than one, or even two, things to say.