I think a certain regularity of work is not a necessity for an employer-worker relationship to be exactly that.
And at a second thought, AFAIK Uber does even expect drivers to perform "regular" work - not "regular" as in "we write 9-to-5 every day into the contract", but "regular" as in "of course you can work as much as you like, BUT if we see you driving too little time for Uber, below a certain threshold that we set at our discretion, don't tell anyone and change as often as we want, our magic algorithm will start disadvantaging you when it comes to handing out rides, oh and actually we aren't acknowledging that this mechanism exists at all, so let's just say this sentence really ended at 'as much as you like'".
I'd only call that "fair" if they assume the position of an actual employer at the same time, offering all the usual benefits of an employment to their employee drivers, especially including a minimum income. If they did, they were free to distribute work as they like, by any crude criteria imaginable, because it's not at all illegal to fully pay an employee for essentially doing nothing. But that's exactly what they don't want to do.
We have what is called "ekstravakt" job positions in Norway which could be called "call in only" positions. You get sick leave based on when you would normally work and you get pension, vacation money etc based on how much you earn.
It's not a problem to implement at all, I was the manager for many youths hired as such in a company I worked for 20 years ago.
The hourly wage for the 16-18 year old crowd was about $12-13 before tax and benefits (+12ish% employer tax that the worker never see).
> Is there such a thing as an employee with random hours?
As any junior employee in retail or the service industry will tell you, yes.
Their hours are random, unpredictable, up to the caprice of their manager and are assigned with very little notice. They also rarely add up to 40h/week.
During a labour shortage, this goes the other way, where managers end up scrambling to staff their store/restaurant, because their less-reliable employees decided to not show up to work, with very little notice.
Not for a lot of minimum wage and service industry jobs. Millions of adults in the western economic world work these kinds of jobs, and shifts can be moved around, shortened, lengthened, or disappeared altogether (via being given to someone else, or because business is expected to be slower). This isn't at all OK, but it's the reality for lots of people.
Sure, how about people who work for Amazon warehouses? They don't have regular shifts or hours... They have to answer a notification on an app in order to secure a shift for the following day.
And at a second thought, AFAIK Uber does even expect drivers to perform "regular" work - not "regular" as in "we write 9-to-5 every day into the contract", but "regular" as in "of course you can work as much as you like, BUT if we see you driving too little time for Uber, below a certain threshold that we set at our discretion, don't tell anyone and change as often as we want, our magic algorithm will start disadvantaging you when it comes to handing out rides, oh and actually we aren't acknowledging that this mechanism exists at all, so let's just say this sentence really ended at 'as much as you like'".