The Bruce Springsteen song 57 Channels (and Nothin’ on) reflects the popular prejudice that television represents quantity without quality.

However, John Landgraf, CEO of the channel FX, argued at a recent industry conference that the medium is now facing a new crisis of supply. He calculated that 371 original scripted TV shows were made in the US in 2014, while the tally for the current year may pass 400. “There is simply too much television,” he said.

Whereas Springsteen was complaining about an avalanche of trash – his sample included the rise of shopping channels on 1980s cable TV – Landgraf’s observations are confined to drama, which generally has higher levels of high-end content. While worrying about this rush of stuff including concerns about rubbish (“it’s impossible to maintain quality control”), he also fretted that gems were being overlooked because viewers will struggle to locate the good shows in the torrent.

This situation – 400 dramas and we don’t know what’s on, to paraphrase the Boss – feels surreal for older British viewers: those over 40 will remember when four terrestrial channels represented a luxury of choice and listings magazines had space to print the names of bit-part actors and assistant technicians. Until the satellite and then digital revolutions, viewers and schedulers in the UK were limited by what was known in the jargon as “spectrum scarcity”, a term that reflected the way governments made broadcasters pay exorbitant tolls to access a road with limited lanes. But, with the super-wide freeway created by the explosions in TV and then online streaming, British producers and consumers of television now face a spectrum glut – and the risk, raised by Landgraf, of an overwhelming level of content.

The comments of the FX boss echo a longstanding concern in book publishing, namely that the supply of titles usually far exceeds the available readers, resulting in most volumes going unread.

A crucial difference, however, is that the crisis of quantity in TV fiction is exacerbated at the moment by the volume of quality. The playwright Sir Tom Stoppard joked recently that he was hoping a long illness would leave him bed-ridden so he could catch up on all the boxsets he had bought. This remark reflected the modern equivalent of the Springsteen problem: a surfeit of modern TV classics and not enough time to watch them.

Despite being a smug completist of Breaking Bad and The Wire, I currently have multiple episodes of Veep, Humans and Not Safe For Work in an electronic stack more dauntingly tall than any pile of unread books that has loomed beside my bed or desk. Another drawback of broadcast stories is that, whereas novels and biographies – with the exception of trilogies and multivolume sequences – stay the same size while they wait for you to get round to them, a hit TV series keeps growing like a triffid while your back is turned. What were four unwatched episodes can easily become eight by the time you next check. Soon, like a lagging runner being lapped, you can be two seasons behind.

Landgraf suggested that the overcultivation of TV shows must lead to a weeding: “My sense is that 2016 or 2017 will represent peak TV in America, and then we will see a decline.”

Again, similar predictions have been made consistently in the book business. There, though, the number of products has kept rising and is now impossible to quantify because of the torrential addition of ebook self-publishing to the traditional methods of distribution.

Due to the huge costs of creating quality TV fiction, it seems unlikely that eTV will have a similar effect on broadcasting. And it’s the economics of screen production that are most likely to achieve the winnowing that Landgraf believes is necessary. With the funding model of Britain’s biggest TV drama producer under threat from the government’s current examination of the size and scope of the BBC licence fee, and the finances of streaming networks still mysterious and unproved, it’s unclear how much money will be available in the future.

For the moment, though, the man from FX is right. There has never been as much drama on TV and, against the predictions of the cultural snobs who have denigrated television for so long, there is too much good stuff for any viewer – apart from a childless insomniac with unlimited free time – to get through.