It's not necessarily transitioning of whole products, but big IP blocks and pieces. AMD, for example, has RDNA2, Zen 2 and 3 in their 6nm chips, because they could reuse 7nm designs. And that's a big part of why transition from N7 to N6 is so fast - it may be mostly new products, but it's a lot of 7nm IP as well. Although this in theory makes porting whole chips to 6nm even easier, if someone wants it, like Sony did. I'm not insisting it happens a lot, I'm saying it's easy, design level compatible, cost effective and saves die area, which you disagreed with.
As for "6nm being a solution to shortage", I repeat - there are no separate 6nm fabs nor production lines. It couldn't be a solution, because it's the same capacity that was mostly taken by 7nm products back then. Everything from 7nm family is produced in the same fabs using mostly the same manufacturing steps, devices, resources, with only relatively small differences. It's a single process family, TSMC reports it's market /production share, utilization rates and revenue together, experts say their wafers are very similar in prices, all of its member share fabs etc. And this is why TSMC can quickly replace 7nm output with 6nm as clients transition. N6 became the most popular 7nm-class process in like two years without wasting 7nm capacity or having to invest in separate 6nm capacity to satisfy demand. They just naturally switched more and more fab output from N7 to N6 as more N6 and less N7 orders were made.
