There are very, very different perspectives on this depending on what deities and what traditions we are talking about. For one, the majority of neopagan religions don’t render cult to deities the same way that they were culted back when and where they came from, so servitude in most neopagan contexts might be more of a matter of choice (and voidable) than obligation.
In afro-brazilian orisha religions (and that may well apply to the same in other countries), an initiate gives their “head” to their ruling orisha. It literally means that that entity now owns, and to a good extent controls, your destiny. Of course, the idea isn’t merely offering oneself in servitute in exchange for nothing. It’s assumed that the god will help a person through life. I’d also highlight Vodou’s “sevi lwa” and what it means, in practice.
But yes, the dynamics is unarguably one of control. It’s not as simple as slavery for favors because even the concept of destiny in these same religions says that freedom isn’t literally what it means. Though it’s not incorrect to say as much.
