Additionally, good on your baristas for being flexible, though the corporate office might object and come down on them if they found they were offering this, as they're either losing money or making less money serving you then they'd make if they served a different customer - so the time to make your drink would be particularly economically suboptimal.
Anyways, these are mostly fiddly points and my original comment was less about the fact that businesses always did things like this... and more about the fact that they do have the right to refuse. If you go in one day and a different barista is behind the machine, they may refuse your request and so it goes - alternatively maybe your usual barista got a talking to from management and can't do it any more. Either of these cases work, declining partial service is an option for a business... in fact, declining normal service is also usually an option, maybe you're going to a ramen place that's open until 7 and arrive well before, but the owner has a headache and is closing up at 5:30 when you walk in - you're not _owed_ service.
The only exception to this is cases where people have historically been terrible and the government has specifically stepped in, if you were black and starbucks refused to serve you after serving a white customer and before serving another white customer then the onus would be on them to rationalize why they refused service (and they'd probably end up paying a hefty fine or being targeted by a lawsuit).
In a lot of ways you can't really compare it to real world examples, because even within corporate chains individual employees can just say fuck it and choose to give the customer a discount or a custom order or allow something they shouldn't.
With an online business like Spotify that utilizes algorithms and automatic actions, this is unlikely to ever happen.
Having worked in a few customer service jobs, or hell even now where I work now, you'd be surprised what customers think they're owed vs what they actually are and how often they do end up getting their way.
In some ways maybe it's because of this people take this mentality onto the web and expect to be able to do the same things.
The real world usually ends up being a lot more grey than the black and white of the legalese and terms and conditions of the internet.