We have been renting our home for about 9 years. The carpets were new but quite cheap and after about 5 years they were frayed and had humps where they had stretched. We paid for a replacement ourselves at no cost to the landlord as we prefer to be self-sufficient. 4 years later these are now in a sorry state due to a combination of cheap carpets laid on old underlay, and with it being a small house (bungalow) where EVERYWHERE is a high traffic area.
Is it unreasonable to ask my landlord to replace the carpets?
No not unreasonable. If you have been a good tenant and the LL has any sense, after 9 years of cheap carpets and poor underlay, they should be fully prepared to replace it. An investment in better quality (if can be afforded) would pay for itself.