I may be wrong about this (and I'm sure plenty of folk will tell me), but I'm convinced I've read that a brand new pair of tyres should be fitted to the back axle and the part worn ones on the front of a front wheel drive car. Something to do with the back end loosing grip more readily in the wet.
this is the correct and current advice.
you are right that if you put brand new tyres on the front with worn on the rear then the car is at increased risk of oversteer and nasty accidents. - entering a corner then coming off the power due to an issue or braking for example has significantly increased potential for loss of control due to differential in tyre performance (in the wet at least). - que flashbacks to my pug 205 1.9gti days..
It also means, that you tend to through the tyres in in a FOFO manner. (first on, first off)
this avoids potential for having aged tyres on the rear, and if you are going to burst a tyre on a pothole (usually the fronts) you did a least get some wear out of them..
and finally, this approach tends to mean you buy tyres in pairs, rather than less often but needing to replace all 4 at once which will be a shock to the wallet if not planned for.
My own personal opinion:
I would say if the rears are more than half worn, then definitely move to the front. If less than half worn, its still good practice to, but you are an adult and so you can make your own decisions. (but put the new ones on the rear anyway)