The explanation is given in NY FED - The Treasury Auction Process: Objectives, Structure, and Recent Adaptations.
The Treasury first adopted the multiple-price format when it initiated
bill auctions in 1929 and it continued to use that format when it
introduced auctions of coupon-bearing securities in the early 1970s.
However, when the auction process came under scrutiny in 1991, public
officials became interested in alternative formats that might appeal
to more investors and that might lead to lower financing costs.
Several academics had suggested earlier that single-price auctions
might reduce financing costs (see Carson , Friedman [1960,
1963], and Smith ). In a single-price auction, a participant can
bid its actual reservation yield for a new security, that is, the
minimum yield at which it is willing to buy the security. The bidder
certainly has no reason to bid a lower yield, but if the auction stops
at a higher yield it will get the full benefit of buying at that
higher yield. In contrast, the multiple-price format encourages a
participant to bid higher than its reservation yield in hopes of
getting the security on more favorable terms.
Box 2 explains the results from the test auctions that the treasury conducted.
The Treasury produced two empirical studies of the results of its
experiment with a single-price auction format: Malvey, Archibald, and
Flynn (1995) and Malvey and Archibald (1998). The studies
calculated—for both single-price and multiple-price auctions—the
difference between the auction yield of a security and the yield at
which the same security was trading in the when-issued market at the
time of the auction. A positive difference indicated that the
securities had been auctioned at a yield higher than the one at which
they were trading in the when-issued market. For securities auctioned
in a multiple-price format, the average difference was statistically
significantly greater than zero. For securities auctioned in a
single-price format, however, the studies were unable to reject the
hypothesis that the average difference was zero. These results suggest
that moving to a single-price format would lead to lower financing
If you continue reading you will see that the results are not unambiguous. Nonetheless, the underlying idea is that this design should lead to lower costs and there is some evidence that it indeed does.