This feels like when I tell my wife I think they should
Things that come to mind are +/-, shots blocked, offensive vs defensive zone shifts, hits, stickchecks, pass blocked, goals against vs goals for...
No one really cares about defensive metrics anymore; most of the major awards are about points these days (Selke, Norris, Calder) without really any defensive measures thrown in. When was the last time a good defensive-defenseman was up for a Selke like Slavin or Tanev or Brodin? They might get one or two votes, but never in the top 3. Slavin got close with a top 5 vote.
Jackman was really the last defensive defenseman that won the Calder and was in the top 3 of voting.
Most people don't care if a center is good at defense either.
This may blow your mind, but stats are used for stuff other than awards voting.
What a weird take that "most people don't care if a center is good at defense" either, what does that statement even mean? They get less attention? Sure, offense is glamorized, that's not news in pro sports though.
Even casual fans would want their centers to be good at defense, go poll 100 fans and ask them "would you prefer your centers to be good, bad, or you don't care" and I'd be shocked if more than one or two jaded clowns answered "don't care."
What fans are like "yeah sure, give me a guy with Zach Aston Reece levels of defense over Kopitar, who cares?"
This thread is a really weird, awful take to do away with stats.