It depends on who you talk to about this. Remember riding the single speed bicycle as a child and wishing for gears and hand brakes? Now do this on an adult size bicycle. The fixie will let you pedal backwards, though.
I believe that using the legs to stop and slow down the bicycle will put stress on the knees. There are good and bad points to consider as well as where this bicycle will be ridden: road, track or trails, on hills or level surfaces.
There is a lot to consider before making a purchase; therefore, I strongly suggest renting one for a day.
I will stick with my bike with gears and hand brakes. When I want a good workout to gain strength, I keep the bicycle on the hardest gear. The options make good safety sense to me, as well.
Enjoy your biking experiences.
Its more of a cultural thing at the moment. You are more at one with the bike on a fixie and people can do tricks with that control. However, I rarely see them on serious MT. trails or long distance road rides. Shiftable gears really come into play in these disciplines. Fixed gears are great for local commuting through traffic and aren’t as fragile to curbs and such as traditional road bikes. RIDE EVERYTHING, and then determine what best suits your riding style. My last ride was a fun 28 miler and I was very happy to not have a single fixed gear when riding in traffic 25-30 mph zones. But, I commute to the city, not through it as much. On a Mt. trail… use what feels best but I pity the fixies on uphills.