Cheap knives
And replace them just before Christmas each year (when you often have extra people around anyway, to use the extra knives you have for a month).
At £1 for a knife that will hold an edge for a year (dishwashed as normal, sharpened as required) an "expensive" knife is probably going to have to outlast me to be an economic decision - and that is ignoring any time I take looking after it "properly".
Nice knives are nice, no doubt, but with the effort some people are going to above?!!
For a chef, then yes - buy decent knives.
For a home kitchen - go for ease and replace the cheap knives just before Christmas.