From Wikipedia

The crucial factor in the size and shape of the Shuttle orbiter was the requirement that it be able to accommodate the largest planned commercial and military satellites, and have over 1,000 mile cross-range recovery range to meet the requirement for classified USAF missions for a once-around abort from a launch to a polar orbit. The militarily specified 1,085 nmi (2,009 km; 1,249 mi) cross range requirement was one of the primary reasons for the Shuttle's large wings, compared to modern commercial designs with very minimal control surfaces and glide capability.

I heard some opinions that the wings could be diminished if the requirement of 2000 km cross-range was not forced. So weight and complexity of Orbiter could be reduced.

But less wings would lead to higher landing speed of Space Shuttle. It already had landing speed about 340 km/h, much more than conventional aircraft.

Could Space Shuttle's wings be diminished?

My personal guess they could not..

The question suppose all the rest requirements of actual Space Shuttle are not changed (payload mass, payload bay size, etc).

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    $\begingroup$ NASA did some research into lifting bodies: aircraft that have minimal wings and derive most of their lift from their body shape. nasa.gov/centers/armstrong/news/FactSheets/FS-011-DFRC.html Landing speeds were comparable to normal-winged aircraft. $\endgroup$ – Hobbes Jul 3 '18 at 13:08
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    $\begingroup$ Shuttle made several (4?) high-speed S-turns early during it's return. To generate the single-orbit-return cross-range they would have made them "anti-NASCAR style" (only turn right). But even when headed straight in, they still had to make those turns to manage lift & drag vs descent rate. So that turn capability turned out to be helpful even for a normal landing. $\endgroup$ – Bob Jacobsen Jul 3 '18 at 23:27

Dennis Jenkins' Space Shuttle1 has a good summary of the development history.

Original Orbiter designs had a straight, high-aspect ratio wing. But the charts in Jenkins show that after the first appearance of the 40,000 lb payload weight requirement, the designs changed to delta wings and stayed that way, even for lower payload weight requirements.

Design configuration summary enter image description here

Page of design configurations at the switch to delta wing enter image description here

But retrofitting a new, smaller wing on to the existing Orbiter? That would have been completely impractical.

1 I have the 1992 edition, not this awesome three volume boxed set. At least, not yet...

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    $\begingroup$ I just picked up the 2002 edition of the Jenkins book, and WOW. $\endgroup$ – Russell Borogove Jul 19 '18 at 18:20

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