I've bleached old grey microfibre inserts but I don't like to use chlorine bleach regularly because it's pretty nasty stuff to be pouring down the drain. It didn't make as much of a difference as I expected really (to staining/dingy grey colour), though I probably could have done it again and might make more of a difference if done regularly. It would probably invalidate a lot of your warranties though, on other brands that don't recommend it.
I do use a lot of 'eco bleach' (usually sodium percarbonate e.g. Clean & Natural Laundry Bleach, Ecover Laundry Bleach, Violet's, same kind of thing as OxyClean but without added nasty chemicals). It does take out stains on things quite well I find if done quickly and it seems to brighten general white washing quite well.
I don't think bleach should be needed for preventing build up, it'd be better to work out your washing routine rather than using bleach to fix it.