The idea of replaying moments of our lives reminds me of a Black Mirror episode from Season 1. "Set in an alternative reality where most people have a 'grain' implanted behind their ear which records everything they do, see or hear. This allows memories to be played back either in front of the person's eyes or on a screen, a process known as a 're-do'." Without giving too much away, the episode explores how new solutions to human-problems create unforeseen issues.
I think that the efficiency of technology shown in TV shows and movies shouldn't be assumed to imply something about the world therein, unless it's explicitly called out in the work itself. The writers are much more likely to have gone with something because it sounded cool than because there was a sound technological reason for it. The bit in the matrix where someone refers to someone else as "copper-top" is an example, I think.
To address your point about Fifteen Million Merits, the way I had the excercise bikes framed coming into it, the "system" being presented is a prison (a microcosm of the larger society outside), and riding the bikes is part of their punishment/sentence.
This is what the episode all the more disturbing to me. This would be the far-west's answer to a demand for less retribution-oriented prison designs, like a virus becoming less deadly so that it can infect more people. (How many on Hacker News would tout the virtues of free services as "you only have to watch ads, you're not forced to buy anything"?) You have "free choice", but it is only within a heavily curated model of illusory flavors; yet the vast majority of prisoners in this system are content, even euphoric, within it.
As Eddie Izzard put it:
> I know a lot of people who'd love to be under house arrest! They bring you your food... "Just stay here? Oh, all right. (laconically) Have you got any videos?" You know, you just sit there all day...
My take on the role of excercise bikes in the Fifteen Million Merits episode is that they're more of an abstract representation of what is most likely a meaningless job.
It's possible that the bikes are used to generate electricity, but that would be very inefficient and, also, not a very creative interpretation. Maybe they're part of a fitness experiment - the participants have an exercise regiment that they keep and are being monitored for the effects the excercise has on them. In return, they are provided with lodgings and food. After all, people have been paid for weirder things in modern times. I can think of a few more scenarios where the bikes are a part of some data gathering/social experiment thing.
Overall, I think, Black Mirror has a trait that distinguishes good fiction from bad - it manages in each episode to create a world that is abstract and unfamiliar enough to play by its own rules, but at the same time, allows parrallels to be drawn between the fictional world and our reality.
*http://en.wikipedia.org/wiki/The_Entire_History_of_You