With the 787-10 stretch, Vedad Mahmulyin (a Boeing engineer) saved the company millions by implementing a software solution that negated the need to enlarge the horizontal stabilizer.
Software again proved useful with the sizing of the horizontal tails. As a stretch of the 787-9, textbook aircraft design would suggest the 787-10 would need larger horizontal stabilisers, offsetting the effect of the longer fuselage on pitch control. Instead, Boeing engineer Vedad Mahmulyin used software to increase the effectiveness of the existing stabilisers. Boeing gave Mahmulyin an internal engineering award for solving the problem.
Flight International (27 Mar 2018)
When a plane is shrunk, that is usually the case because of the reduced moment arm. When it is stretched, the tail volume is retained if I understand this comment about the DC-10/MD-11 stretch correctly:
Isn't the tail of the MD-11 smaller because it has a longer lever arm? The tail volume of both aircraft should be quite the same. Also, any FCS cannot help to trim the aircraft over a wide range of cg positions, and it is this trim range which drives tail surface volume. @PeterKämpf
So why would a stretch variant need a larger horizontal stabilizer?
Also, from an interview with Mahmulyin:
Mahmulyin figured out he could use software to tell the wings and the stabilizers how to fly together, "As opposed to having to produce all new horizontal and vertical stabilizers," he said.
What does "flying together" mean? (This is an optional question and does not involve proprietary information.)
Update and accept reason
The reason for asking why would as opposed to why does is I was not aware of any previous [jetliner] stretch requiring a larger horizontal stabilizer. For example, all the DC-8's from shortest to longest (almost the same stretch as the 787-10) retained the horizontal stabilizer throughout:
But then I finally recalled a situation where it has happened, the 737 Classic, and the reason given is the "fore-and-aft loading flexibility", in other words the cg range, and that's why I'm accepting @jwzumwalt's answer.