If you add that saved .lyrx file to Pro, does it load up in the map as a valid OD Cost Matrix layer (ie, it shows up in the map, it's not broken, and you can see the purple OD Cost Matrix tab)?
When you use the Save To Layer File tool, sometimes it gives you two option of which layer to save that have the same name, like "OD Cost Matrix". The first one is usually the actual Network Analyst layer, and the second one is a regular group layer representation of the layer. If you save the second one, it loses its special Network Analyst stuff. I realize this is kind of strange, and I don't know why it works like this, but it seems possible that this is what happened to you.