It took awhile for me to pull my act together after 'living' myself a nice american dream over the prior decade and as such I had a hole to climb then fill.
The first refi improved cashflow which was used to help eliminate some high-interest bad debt - however I still didn't have a gameplan as my financial advice sources were... terrible... and my cashflow was generally negative.
The second refi was cashout and very minor cashflow improvement. The cash-out eliminated some more bad debt. At this point I had a fairly good starting plan to track/optimize spending and invest the difference. I hadn't found FI literature, but I'd run enough math to know that a path towards FI was possible. Within a couple of years I was checking refi for investing and was developing a fairly broad understanding of the markets (both stock & real estate). I went from massive negative networth to a 50+% savings rate over this time constantly seeking efficiency improvements to spending, earnings, and investing. I made mistakes, but learned a great deal.
This last refi, the cash-out was invested. The cashflow allowed, for the first time, a cashflow positive REI option. I also stepped away from my historical industry to help build a business from scratch as my spending was optimal enough that my investments could cover years of an attempt.