I can't imagine any reason to require mesh for a routine breast augmentation procedure. If you needed a breast lift or a breast reconstruction, I could see the possible need for mesh. Mesh is expensive stuff, so I try to avoid it if I can.
It depends what you mean by mesh. If it is a synthetic or non-absorbable material, I would highly advise against the practice. That said, biologic materials (called acellular dermal matrix or ADM) made of human or in some cases animal skin are less likely to reject and cause long term problems.ADM is usually reserved for more complicated cases where the breast lift or implant needs additional support.