Maybe we just have a failure to communicate. The expander, which is part of the decapping stem on a Lee .303 die, isn't itself called a "die". (An "expander die" is a complete assembly, expander and die body, with the sole function of expanding case necks, and not normally part of a die set for bottleneck rifle cases. See photo below.) It certainly does collect crud from the neck interior and when really cruddy we can encounter strong resistance to withdrawing the case, often accompanied by an unpleasant screech. Treating neck interiors with a suitably-lubed bristle brush eliminates this problem very effectively. Grit on the decapper/expander doesn't normally get dragged outside the case in sufficient quantity to cause problems inserting the case into the die. Excessive liquid inside-neck lube can build up on the stem immediately above the expander and may spill onto the case mouth and the die body interior. (This is why novices are better off using dry lube until they learn how much liquid lube is "too much" - your fine picture of the expander shows you're applying far too much liquid inside the necks.)

"In what way am I hard to convince? . . . Been listening to you and following your advice." Well, on 1/8/10 I advised you to polish and clean your sizer. Had you done so, we could have moved on to something else a week ago. I like Lee dies and own about a dozen sets, but I've yet to see a new Lee rifle sizer that arrived with a first-class interior micro-finish and wouldn't benefit from a good polishing and cleaning. (New Lee expanders also need some final polishing, which will reduce the brass residue you've observed on yours.)


Expander (right) plus die body (center) make up an "expander die".
(Pliers and case on left irrelevant to this discussion.)

In bottleneck-style cartridges, the inside of case necks requires lubrication to avoid friction as the sized case is withdrawn from the sizer/decapper/expander die assembly. My experience is that the powder/primer residue is not a primary issue. Given adequate lubrication, the presence or absence of the sooty residue in the neck has no significant effect on friction. The key is adequate lubrication. Various dry lubes can provide this with no chance of contaminating powder or primers. Graphite, molybdenum disulfide, and finely-ground mica are commonly used by dipping each case neck before sizing into a small container with about 3/8" of lubricant. Enough of the powdered lube adheres to the neck interior to reduce friction to an acceptable level, despite the thin layer of residue usually present. Dry lubes may also be applied with a small brush, but this is generally less effective at leaving an adequate quantity inside the neck. Liquid or colloidal lubricants can also be applied with a brush or spray, but learning to control the quantity of lube in the case neck takes some time and experimentation. Too much oily/greasy lube inside the case will contaminate powder or primers, degrading performance, and can also cause powder to stick in the neck during charging, bridging the opening and making a mess with automated charging equipment.

Below the case neck, there is normally a fairly thin but tenacious layer of residue adhered to the case interior. It is hard and rather brittle - bits of it commonly break away from the brass wall during sizing because it is less elastic than the metal to which it adheres. If you invert and tap previously-fired cases over a clean sheet of paper right after full-length sizing, you'll soon collect a small quantity. You'll also find that some is ejected along with the primer and falls onto the ram and press frame wherever the spent primers go. Aside from getting your tools and bench slightly dirty, the residue appears to do no harm. Although at bit more is added to the case interior with each firing, even after 30 or more firings it hasn't accumulated enough thickness to alter either appearance or function - probably some of it gets burned or carried away during combustion of each subsequent charge. (Black powder residue is another matter, it is thick and corrosive but readily soluble in water and cases for such use are normally washed after firing.)

I think it's safe to assume your .303 cases were probably not fired with black powder loads. Very few handloaders today would choose black for a cartridge that's been successfully employing smokeless powder for over a century. Every so often, however, some poor fool tries it and quickly discovers that black powder fouling is a real problem in 10" twist Enfield rifling unless you swab out the bore between shots. Don't ask how I know this!