A few things. The business's objective is to encourage the user to add new feeds. Since the content (of the feeds) will drive their motivation, the best you can do (without research) is to provide the tools for them to do so.
I've encountered this situation many times - where the business wants to "hide" or "make it difficult" for the user to perform an undesirable interaction. The fact is that the interface alone will not change the user's desire to unsubscribe just by coming to this page.
If they want to unsubscribe, give it to them because hiding the mechanism and assuming the user is going to find the unsub mechanism might lead to unintended consequences such as nobody being able to find it and then they flood the customer service number or inbox - creating another headache (separate topic).
Stakeholders tend to look at the interaction from a smaller frame of reference and this is where I tend to present the big picture to them and reference other consequences - "sure we can hide the unsub link but keep in mind that all of the utilitarian interactions on the page are housed in the upper right and the expectation might be to find the unsubscribe mechanism in a similar position".
Also, you were right when addressing the bulk unsub pattern but to do this you'll need to pull out the unsub link into a single button and add a Boolean selection option to each of the items (like a checkbox or toggle). Since you have no real research with your own users at this point, you might want to align with a known and understood pattern.
One last thing, hiding that unsub link made me immediately think of this as a dark pattern candidate and also it brought to mind a UI mistake common in the early days of design - "mystery meat navigation".
All in all though - your take it correct in noting that something just isn't right about this interaction.