The Lure of Las Vegas, BBC Two

“The Mob made Vegas,” says its mayor since 1999, Oscar B Goodman. And he should know, having defended plenty of mobsters in his time when - he and I are equally quick to point out - he was a defence attorney and didn’t know what they were really up to.

What a trick presenter Alan Yentob missed here; he could have simply chatted to this wrinkly, wily New Yorker transplanted to the Nevada desert and The Lure of Las Vegas (shown as part of BBC Two’s Vegas night), produced and directed by Janet Lee, would have been a whole lot more entertaining.

What we got, this being an Alan Yentob documentary, was a lot of shots of Alan Yentob talking, Alan Yentob walking, Alan Yentob driving and Alan Yentob lying on his hotel-room bed thinking out loud. Which is a shame as Las Vegas is an extraordinary American city, a contradiction in every way; a place called Sin City that was settled by the Mormons, a one-time Mob town that has transformed itself into a family holiday destination, and a location once known for offering quickie divorces that is now the country’s top wedding destination (there are 120,000 nuptials solemnised there each year).

Yentob was trying to do too much in 75 minutes - part travelogue, part arts documentary, part history programme - and ultimately disappointed on each score, offering us only tantalising glimpses of what The Lure of Las Vegas might have been if presented by a journalist with a nose for a story or an arts critic with an interest in the subject.

Vegas is, after all, a film-set in its own right, and has invented both a genre of pop art in its neon-bedecked Strip and a style of architecture - “architainment” - in its fantastical hotel creations, which reference everything from North Africa and New York to Venice and the Pyramids. These subjects all had a talking head to give a sentence or two to explain (sometimes rather dismissively), but Yentob, while almost ever-present, appeared often irritatingly unengaged.

Vegas is also known as an outdoor museum of American culture, and is a city that once boasted a Guggenheim museum and still has a restaurant with Picassos on its walls. But not a flicker from the presenter; even when he visited a junk-yard where he came across old neon signs from long-demolished hotels and casinos - pieces of Las Vegas history that count as its crown jewels - Yentob appeared to be about as turned on as a 20-watt bulb.

Many of the above - not to mention the honourable Mayor Goodman - would be worth a programme in their own right, but instead we got the usual Vegas by numbers: archive footage of its massive post-war development by the Mafia, the Rat Pack, Elvis and Liberace, who established it as an entertainment centre, present-day wedding chapels and gaming tables, but no development of a central thesis.

Some more original strands certainly excited my interest. For instance, Vegas’s increasingly monolithic, monochrome architecture is, we were told, a sign that a city once known for its hedonistic excesses is now aiming to go upmarket and attract rich, celebby high-rollers who value their anonymity at the gaming tables and in spa hotels. And I shall be listening to The Killers’ song lyrics rather more carefully after hearing their frontman Brandon Flowers talking briefly about how being brought up as a Mormon in Vegas (followers of the faith form 12 per cent of the local population) has influenced his music. Listen to “Somebody Told Me” with that knowledge, by the way, and it takes on a different meaning.

Fascinating, too, but surely deserving of more airtime was Jerry Weintraub, one-time Las Vegas music promoter and producer of Ocean’s Eleven, Twelve and Thirteen (2001-2004), the first of which was a remake of Ocean’s Eleven (1960), in which Frank Sinatra et al made criminals look super-cool. He visited the set of the 1960 film, as he knew many of those involved back in his native New York, and two of Weintraub’s Ocean’s films are a love letter to a place that clearly fascinates him to this day. Ultimately, though, The Lure of Las Vegas was a frustrating watch for anyone who knows this weird and sometimes wonderful city, and for anyone who hasn’t been there its attractions remained unexplained.

• Watch The Lure of Las Vegas on BBC iPlayer
• Find Ocean's Eleven and Ocean's Eleven-Thirteen on Amazon