Ok, I'll try and use an example from financial services:
Disclaimer: Never worked in financial tech, I have thought about this problem for 5 mins. This is unlikely to be an optimal solution to keeping a sorted set of distributed data. I'm just trying to show how basic knowledge of data structures helps in the field of distributed systems.
Lets say you need to keep a sorted set of sooooo much data that you cannot keep it all on one machine. I would imagine all financial services firms have some custom datastore which has "potential buy orders" and need to keep them all sorted by profitability to efficiently search/insert/remove from that datastore.
In such a situation, my instincts would be to create a distributed, redundant Heap. Now, how do you build a distributed, redundant Heap, without understanding how a Heap works? How do you even know what to look for if you don't know what a Heap is?
Now, lets say you've built it such that each node in your distributed network acted like a node in a Heap, and the left "pointer"(i.e. url to other computer) meant "less than" and the right "pointer" meant "greater than". Now you have this data store in production and all of a sudden you realize performance worsens over time... "WHY is this happening? Is there some memory leak?". You investigate and realize that all of your data isn't being distributed evenly! "Do I need to like.. shuffle the data around? How do I get it so that the data is evenly distributes?"
At this point if you do not know what a red-black tree is, what do you even google look for? Lets say you dig around for a while and find out about re-balancing trees. Now you have to implement it, and eventually you figure out that one of the best ways is to color your nodes. When a future colleague/manager asks, "What is this system, please describe it to me?" wouldn't it be nice to just say "Oh visualize it kinda like a distributed red-black tree. It holds XXX data, and ensures that it is always sorted and re-balanced for optimal performance."