A life jacket should be encouraged because swimmers get tired and swimmer drown. I am amazed at how many parents are told NOT to use a life jacket when in open waters. It is necessary when swimming outside your normal environment.
Please just take note that just because your 9 year old can swim the 200m pool does not mean that they are safer or Okay in a river/lake etc at the same distance. The environment and water current is very different and the swim schools should be teaching you that a life jacket is your back up to when you get tired. As for vests I dont like them as they keep you vertical as opposed to a life jacket keeps you on your back to float when you are tired, y ou are able to swim with a life jacket forward motion but when you stop it will allow you to rest. A vest will bob you up and down like an apple, risking the inhalation of water.
I really wanted to highlight what hannahbug has said here. As a person who grew up having swimming lessons and being a very good swimmer who holiday'd on a lake please take this advice. It is so different swimming around in a lake (even the shelted valley style lake we swam in) then swiming in a pool. Yup my child won't be wearing a life jacket or swimming vest or floaties in our pool - as they will only be allowed in when we are in the water with them, but the open water will be a totally different story. The smaller life jackets (pfd 1's) have a strap on them for younger/smaller children which stops the jacket coming up (I know alot of people don't like) For them to be comfortable with life jackets though means that we will have to do "lessons" with them in our pool from a young age with them. We will have to get them used to wearing them and how to rely on them (ie stop swimming and you will float onto your back) Much better doing it in your own pool at swim school then out in the open when something goes wrong and the poor child panics