I don't actually have a definitive "because" for your "Why." You see, I wasn't there. Nope, not present nor accounted for. Was nowhere to be found. Wasn't even a gleam. I digress.
Six guns (you know why) originally (Cap Guns) had a little stud (no, not Sean Connery) between chambers and a corresponding little slot in the hammer face, upon which to rest the hammer (you knew this....right!). Simple and effective. Six up was no problemo.
Then, along came the cartridge guns. Suppositories, more or less. Where the little slot in the hammer face should be ...... TA DA ...... Firing Pin. What to do, what to do, what to do ..... Dunno. Firing pin inna way of everything. Then the Ah Ha moment. Just rest the firing Pin between the rims of the Suppositories. Simple and effective. Except ..... it's still possible to turn the cylinder under the firing pin. Why would you do that?? Pretty stupid. But we needed a better way. Simple. An empty chamber, Hammer down on the empty, and the cylinder is locked. Can't shoot yourself inna foot (yes you can, it's just harder).
Now .... as a point in case. Whoops, "Case in Point" the modern iteration of the self-contained Cartridge Conversion Cylinder (R&D) has an excellent solution. Large bore R&D cylinders are only 5 shooters. Only wussies, wimps, and the blind need six you see. Those cylinders have an added bolt notch for each chamber. The cylinder rotates, the bolt is allowed to rise into the "safety" slot and all is well. Well ..... Or Is It??? It is an effective and elegant solution. Not only that, it also meets SASS requirement for five shot cylinders to be loaded full up. Cool. Only one drawback. Just one tiny little glitch. Timing. The Hand must be carefully timed to run the R&D cylinder. Once properly timed ..... marvelousness will happen
Oh, wait, the OP wanted to know why safe 6 up carry wasn't included in the original design of the "Six Shooters" of the day. Well, actually, I don't have the faintest idea what that little detail was ignored. No Clue. Wasn't around to ask the question either. So ... in all fairness, your guess is as good as mine. Burma Shave !!