The hair on your unit won't get as oily as it used to because its not getting fed by the follicles.
You can always wash your natural hair more often and leave the replacement hair for alternate washes.

There is the recommended amount of washing and then there is what people actually have to do.
If it needs washing, then you'll have to wash it as frequently as you need to.
Just be gentle.

As well as shortening the life span of the unit, washing (or even getting it just wet) weakens the bond, meaning more frequent attachments.

So in the end, you work out whether its better to constantly have a squeaky clean scalp & extra expense & maintenance or visa versa.

The best regime will be somewhere between the two.