I don't know about "breaking in". New textiles often have sizing, which is a compound that aids in the spinning / weaving process. That should come off in the first wash though. I wash my white set in hot water and tumble dry with a cupe wool dryer balls. I don't use fabric softener on anything, because I feel like it makes clothes dirtier, but some people really like fabric softener. So it's a choice.

I have Red Land sheets that I've had for about 6 months. While I think they feel great, that are not going to ever feel like a 600 micro thread count sheet. They are substantial and weight-ier feeling. They drape differently. They breath differently. I've been very happy with them, no pilling or wear to be seen. I think they have a long way to go before they are flannel soft.

Fabric tends to get softer as it gets some wear and tear. Think jeans that have gotten softer after a year or two. But I think some of that is the fiber actually breaking down. You can artificially create that effect by brushing fabric. You sacrifice length of life though.