I think as learners we should do both: practice without much reflection and focus on accuracy.
When you always care about your mistakes it hinders you. It creates fears, it can make learning a torment and maybe even prevents you from making the language you "own".
When you don't care about them, you have what I do. I, for one thing, often say things like "did you walked" or "does he walks" when I'm typing very fast. I wouldn't do that when I type slowly and I didn't do this years before! My tense inventory is also very poor.
What does this mean? (If I typed it a bit faster I'd type "what does this means":().
I became fluent. But the part of my brain which is "fluent" learned Engish in a wrogn way. Differently from the part of my brain which controls my fingers when I'm slow. This another part of brain is very important maybe. It gives English more feeling. It makes it my "own". It is faster. Less abstract. But it gets it wrong. I developed intuition and it improved my listening skill, but this intution knows little about English verb:)
If I were to fix this I would.... Listen to English. This is what I rarely do and what could help my intution. But correcting my mistakes helps too.
My conclusion is that as a learner I'm at my right to pay little attention to mistakes sometimes. There is an "optimal accuracy control rate" and I'm not sure if this rate is 100%. More likely you should switch between modes. Still it is not very nice to other learners and I'm often ashamed.