I took the pill continuously from 1991 to 1997. After my son was born in 1998, I went back to the continuous pill until 2000 when we decided to have a 2nd child. I’ve been back on the continuous pill cycle since 2001. I’ve had no complications and no problem getting pregnant after stopping the pill. I don’t currently have birth control insurance coverage, but in the past I have and my ob/gyn would call in an 'emergency refill' every so often when insurance balked at the 21 day refill timeline. (Viagra on demand, but keep a strict schedule on those pesky BC pills…)
Women spend less time pregnant now than in the past — so we have more periods over our lifetime than previous generations. We prevent our bodies from doing what it was designed to do in a lot of ways, we alter those processes in other ways — but the idea of preventing your period seems odd or unhealthy to some people.