Amazing Stories is – wait for it – not that amazing. The new Apple TV+ show, released last week, is a revival of a 1980s series that was overseen by Steven Spielberg. The master director is involved with the reboot, too, which arrives back to take its place within one of the big TV trends of the past few years. Amazing Stories is an anthology: a collection of self-contained tales rather than a running series. Such shows can be a haven for experimentation and offbeat excellence and ought to be perfect for our low-attention-span age, where new streaming services seem to arrive each week. But, as modern anthologies become more prevalent, so they become a byword for hokey lameness and a lack of quality control.

Anthologies in the 21st century are led by Black Mirror, a show concerned with the telling of spooky, tech-related fables. Like its ancient precursor The Twilight Zone, its intriguing set-up/surprising twist/haunting moral format can only be done in an anthology: nobody wants a 13-episode season entirely about a weird app, or a forest that turns out to be made of haunted computers, or whatever.

But as the years have gone by, the perfectly turned Black Mirror episode, with a fresh premise and devastating pay-off, has felt more and more elusive. When new episodes drop, it’s wise to wait a few days for critics and people with more time on their hands than you to let you know which is the single instalment you need to catch. The duds, the ones that aren’t San Junipero or Nosedive, recede from view, doomed to appear near the bottom of a hundred “every episode … ranked!” articles.

Mackenzie Davis in Black Mirror: San Junipero, Anne Hathaway in Modern Love and the Twilight Zone director Jordan Peele.

That is the problem with anthologies: yes, it can be good not to have to commit to yet another box set, but the flipside is that collections of self-contained narratives feel innately inessential. When shows employ different writers and directors with wildly differing styles, there is nothing to lock you in and make the next episode a must-see. Unless you are watching something like the Apple TV+ series Little America, which is about the immigrant experience and thus thrives on a diversity of stories, the lack of a coherent, singular voice merely guarantees inconsistency.

Take the 2019 reboot of The Twilight Zone itself, exec-produced by Get Out director Jordan Peele. It’s … OK. Hit and miss. Not bad. There’s one called Replay about a weird camcorder that is pretty neat. Really, though, it is devoid of the era-skewering boldness of the original 1950s/60s show, or even a focused new vision of its own.

Anthologies are better when they are the vision of one creator or team. The trouble is, coming up with a glut of good, individual scripts is beyond almost everyone. Last year’s Amazon romcom series Modern Love was a decent halfway house, with roughly half of it helmed by Once/Sing Street director John Carney, and the whole enterprise anchored by being based on an existing New York Times column that could be filleted for its best tales, even if many of them had a charm that was a bit too flighty and diaphanous for TV. Besides, the series also relied on another trope of anthologies to bring in viewers: guest star roles. Roping in the likes of Anne Hathaway, Tina Fey and Ed Sheeran meant producers could bank on audiences tuning in despite shaky scripts.

That is not to say that the unicorn of the unmissable anthology can’t ever exist. Ryan Murphy has done some of his best work on American Horror Story and American Crime Story (the latter being the umbrella under which The People V OJ Simpson and The Assassination of Gianni Versace sheltered), although that is an anthology in the sense of each season, not each episode, being self-contained, and, in the case of Horror Story, even that is not always true.

‘Anthologies are becoming a byword for hokey lameness’ ... Victoria Pedretti in Amazing Stories, The Cellar. Photograph: Apple TV+

Elsewhere, we are just coming to the end of series five of Inside No 9, the persistent high quality and variety of which has put its writers/stars Reece Shearsmith and Steve Pemberton among the all-time TV greats. Mind you, even there, the more experimental new run faintly suggests that Shearsmith and Pemberton might be tiring under the burden of constantly turning out gems – and they still have another two series to write.

Other successful anthologies embrace their throwaway nature: take Moving On, the recently returned BBC1 daytime series that is designed to be enjoyed with a rich tea finger and a mug of Mellow Birds.

Which brings us back to Amazing Stories, whose first episode, The Cellar – a time-travel tale not unlike the Nicholas Lyndhurst sitcom Goodnight Sweetheart – suggests a pleasant but dated series is on the way, for you to take or leave. Despite a big-budget revival, it’s clear that this, and many other anthologies, should’ve been left firmly in the past.