As a clinician I think the answer depends on what you want to do. If you want to make the best fit or make the best adjustment you can use continuous and squared variables.
If you want to describe and communicate complicated associations for a non-statistically oriented audience the use of categorised variables is better, accepting that you may give some slightly biased results in the last decimal. I prefer to use at least three categories to show nonlinear associations. The alternative is to produce graphs and predicted results at certain points. Then you may need to produce a family of graphs for each continuous covariate that may be interesting. If you are afraid of getting too much bias I think you can test both models and see if the difference is important or not. You need to be practical and realistic.
I think we may realise that in many clinical situations our calculations are not based on exact data and when I for instance prescribe a medicine to an adult I do not do that with exact mg's per kilo anyway (the parable with choice between surgery and medical treatment is just nonsense).
