I know this won't be implemented in TLOU, but perhaps in a sequel it would be.
What I have in mind is this:
If you down someone near special objects, such as a fireplace or a wood chipper, a special icon would appear that, when executed with a button combination (e.g. R3 + Triangle), would unleash a more deadly, albeit a more longer execution animation. Doing these environmental executions would also give you more parts than a normal special execution.
For interrogations, the environmental interrogation would be twice or even thrice as long, but you would get more parts, as well as having TWO interrogations counted towards finding the safebox. We might have the interrogation involve a mini game in order to get the two interrogations.
I was inspired to make this thread after replaying The Punisher for PS2, in which there were special environmental executions. Here's a video showcasing some of those executions and interrogations:
WARNING: These interrogations and executions are brutal. Watch at your own risk.
Would be a good addiction to the game, but if it was to happen it most likely be on one of their next game, they already stated they were limited by memory or something when it came to add more animation if i recall correctly.
And never saw the game in you post, it's bloody violent.