If population rises faster than culture expands your radius, you will have to make specialists (or more settlers). If culture is faster, you will have excess tiles to choose from. This is what happens in civ4 in fewer steps, but culture expands much further than city radius. The concern about production oriented cities is valid. Perhaps this can be circumvented by letting the city expand to tiles similar to those already being worked (i.e. if you work one forest, the radius will expand to another one) or by prioritising expansion to tiles that are being improved (meaning the player wants to work them).