To that extent they are no more a slave to the developer than a person dining at a restaurant is a slave to their wait staff. Sure the water could take extra long to deliver the food but that does not mean they are in control.
To be a slave the other person needs to be exercising control over you.
As a developer, ever try to tell marketing that they can't do something for technical reasons, scheduling, or because it is just a bad idea? Extreme example, the way I have seen it work mostly:
1. Marketing wants to make all advertisement autoplay audio
2. Development says: we are busy until next week working on a major deadline, and even if we did have the time autoplaying audio ads is a terrible idea because it has been shows repeatedly to turn off people from your brand
3. Marketing talks to the CEO
4. The ad are autoplaying audio that night and now the developers have to work extra hours because the deadline they were working on still needs to be done.
If anything it is the other way around... devs are a slave to marketing. Marketing says "jump" the devs have to say "how high?" regardless of what else they were working on.
You say:
> This reduces the productivity of digital marketers drastically.
But in reality unless marketing has it's own developers you are in fact decreasing developers productivity and costing the company a lot of time, potentially money, and in many cases decreasing the work-life balance of the developers.
Think about what those developers needed to stop working on to do your task. I doubt they were sitting on their hands.
Edit: with that said, there doesn't mean it's not a problem that needs to be fixed. But put yourself in the developers shoe's for a minute. They don't like the arrangement any more than marketing does.
And it doesn't help when marketing shows no respect for the developers time. Real world example: a marketing team at one of our clients has been working on a TV ad campaign for months. They finished the TV campaign and now they need a landing page for it... they just told us about this landing page Wednesday. The ad campaign "absolutely has to start Friday"... the amount of disrespect you need to have for developers to do something like that is incredible. They new about the need for a landing page for months and gave dev 3 days when they got months to make their 30 second video...