The linkage principle does not depend on risk-aversion, because risk-neutral bidders simply bid according to the expected value they assign to the auctioned object. Having private information not revealed to other bidders, will generate information rents, reduce competition among bidders and lead to lower seller revenue.
Daniel Quint (U. Wisconson, eBay) has some lectures notes where he works out the Milgrom-Weber result in detail, and also gives the following intuitive explanation:
One way to think about this is that bidder’s expected payoff can be
thought of as his “information rents,” that is, the extra surplus he
is able to get by having private information. But in auction formats
where information is revealed which is correlated with his private
information, his private information becomes “less private” in a
sense, so he gets a smaller surplus, and therefore more goes to the
seller. In the logical limit – where information revealed over the
course of the auction fully reveals the highest type – the seller
could simply make a take-it-or-leave-it offer to extract full surplus.