I really feel the need to point this out, consider this...
One bike has a 56cm top tube, a 72,5 degree ST, a 170mm HT, a short reach (75mm) bar with Sram shifters. This bike has a 150mm stem.
The other bike, has the same 56cm top tube, but a 73,5 degree ST, a 120mm HT, a long reach (95mm) bar and Shimano shifters... This bike has a 110mm stem.
The second bike with the shorter stem, actually has sligtlhy longer overall reach to the hoods.
If you buy the frame to suit the stem, you would benefit from considering everything else that impacts steering. Different frame sizes often have different HT angles, and sometimes the forks have different offsets too, actual reach doesn't always follow top tube length, i.e a 52cm frame and a 54cm frame (of the same model) can often have the same reach even if the top tube is longer, due to different ST angles and stack heights.
Also, fork rake and HT angles will determine steering response way more than 20mm shorter or longer stem. But no one ever says "How the hell can you ride a 40mm rake fork on a 72 degree HT, that thing must be as agile as a bus!"