I've been thinking about Elliot's retirement and how he and Liv never spoke after that.
Here's my take: Lots of fans (EO fans or others) don't like that Elliot completely ghosted Olivia. In my mind, the S13 deleted scene with Elliot sending Liv the mini badge and the Semper Fi note is 100% canon because she attaches the mini badge to her gun and we see it there for 2 whole seasons. This might be unpopular or surprising but the more and more I think about how they never spoke again after he put his papers in, the more believable it becomes for me. Most of us know that Olivia and Elliot had more between them than a healthy work partnership. EO fans like me would say they were (still are) in love. They were definitely having an emotional affair by S7 Fault and that didn't stop just because he went home to Kathy when she got pregnant.
Bernie tells us that Olivia "scares the pants off of Kathy", but Kathy knew that Elliot was a devout Catholic and devoted family man (trauma response to abusive father) and that Olivia cared about her and the Stabler kids (Paternity, Swing, Turmoil). Because of this, I think she could overlook some of the warning signs of EO's emotional affair and write it off as Olivia being Elliot's "work wife" or that "what they had wasn't real." And, keep in mind, Kathy didn't like Dani Beck and realized in retrospect that Olivia gave Elliot support and stability that Kathy/another partner just couldn't (Burned).
But when Elliot put his papers in, the work partnership element of Elliot and Olivia's relationship is no longer and all you're left with is a friendship that turned into an emotional affair. For lack of a better way to put it, there is no longer any "cover" for them. Without the work, if they spent time together, it would be because they loved each. Some might say that was just love as friends, but both Elliot and Olivia over the years described their relationship as complicated. I just can't see a world where Elliot could continue to have Olivia in his life without it creating a wedge between he and Kathy and disrupting/ending their family/marriage.
When we see Kathy in the hospital in Return of the Prodigal Son, she says tells Olivia that she didn't believe Elliot when he told her they hadn't been in touch since he retired from the force. Olivia still loomed large in their marriage in the intervening 10 years even when she was gone from their lives. Like, imagine if she'd stayed in Elliot's life (and therefore Kathy and the kids lives). Things might have gone very differently.
The TL|DR is that without their shared work, it would've been really hard for Elliot and Olivia to be and stay just friends. Elliot knew it, Kathy knew it, and years later as she works through the anger and hurt, Olivia has got to realize it too.