I use a flexi sometimes and agree that with common sense and a knowledge of the pitfalls, they are fine.
Mine is a thick tape rather than a string so it's no thinner, harder to see or grab than a normal lead. It's also MUCH easier to untangle if it gets wrapped around bushes.
Near busy roads I would never trust the locking mechanism and so have my thumb actively pressing the button, the tape then feed into my other hand which grips it like a lead so my hand is the first restraint the dog/lead has and the handle is just a back up.
Near other, quiet roads I would still always have my thumb on the button rather than trust the lock.
Only used with a harness and clipped to the back d-ring.
In open spaces, I keep an eye on how much lead the dog has used so that I can recall her before she hits the end of it at full pelt.
To me, this give me as much safety as with a fixed lead but gives the dog a lot more freedom in the countryside (she is a Jack with not-brilliant recall and a high drive to chase anything that moves).
Most professional organisations would require a fixed lead because people don't always think of the dangers of using a flexi and negate them. In training circumstances a fixed lead is often easier to handle as you don't have the big plastic handle that pretty much takes up a whole hand and doesn't leave it free to do anything else. A fixed lead may allow this if the dog is not pulling and is under control.