The fact that a piano can go down to low "A" depended entirely upon the railroad and shipbuilding industries of the 1800s. It had little to do with the wishful thinking of artistic considerations. Read on and I will explain.
I had so many comments to make that I decided I needed to add another answer. @RockinCowboy cited one lone source that implied that the expansion of the range of the notes on the piano was in response to the desires of composers for artistic reasons. I don't agree. Google history of piano and you will find many sources that paint an entirely different picture. You will find many timelines listing technological innovations by builders. You won't see much of anything said about what the composers wanted or requested.
This can be clearly seen: For centuries harpsichords were made of only a wooden frame, and the only available material for strings was plain brass wire. The range of notes stayed the same, at 4-1/2 to 5 octaves. Even the invention of the piano could not go beyond that. The earliest pianofortes in the 1720s had a plain wooden frame strung with plain brass wire, and the same 5-octave range as the harpischord. They stayed that way for almost another century.
I'm sure that composers in Bach's time wanted more notes on a keyboard, but it was practically speaking impossible to build a larger keyboard with more notes.
Harpsichords with a full 5 octaves had very long frames to accommodate the plain thin brass strings that had to be very long to play those low notes. The next innovation was to create wound bass strings -- a plain brass core around which another brass wire was wrapped. That helped a bit, but the wound brass strings were still too brittle for higher notes -- they would break. They still had poor vibrational properties for those lowest notes. Then there was the matter that a purely wood frame could not handle the additional string tension. At this time nobody knew how to build anything that would perform better.
No, the expansion to more than 5 octaves had to wait for the technological innovations in forging, casting, and drawing iron and steel on an industrial scale. These began to happen around 1810. The Industrial Age dawned. Vast foundaries and factories were developed to smelt iron and steel and cast it, and to build railroads and iron-clad battleships.
It was only from this point that the expansion of the number of notes on the piano was finally able to happen -- and it happened rapidly. It was as if a dam burst.
One innovation that came about this time was the invention and use of iron strings, but they were only tried for a short time, because iron strings corrode rapidly and don't produce a good tone. Later a tremendous breakthrough happened: the invention of carbon steel strings and wound steel strings. This enabled rapid innovation.
Read about the History of Piano Wire at Wikipedia. This will explain a great deal.
Around the same time, new technology for making cast iron bars came into play. Builders incorporated cast iron bar reinforcements into the wooden piano frame. In tandem with wound steel piano wire strings, it was now finally possible to build larger pianos with extra low and high notes.
The next huge leap forward was the invention of the solid cast-iron piano frame (sometimes called the plate or harp), which happened from the late 1820s (Chickering) into the early 1850s (Steinway). This enabled the piano design quickly to expand to its current 88 notes.
I found a great lecture online explaining the physical limitations faced by the first piano, Cristofori's invention of 1720, and how the cast-iron piano frame and steel piano wire strings had to be invented first to overcome these problems.
The ability to build a piano with 88 notes followed after the development of factories that built out railroads that criss-crossed the world, and shipyards that built iron-clad battleships. If you don't believe this, the only other possible explanation would be that the railroad and the shipbuilding industries were dependent upon and got their technology from piano manufacturers. This is obviously not the case.
There were many other technological details of the piano that had to be invented and refined and manufactured as well. These had to do with the action and mechanism of the hammers and the keys, which were mostly all wooden. But these innovations would have been of little use without wound steel piano wire and the cast-iron piano harp. That is why these innovations appeared alongside the appearance of iron and steel in piano-building, and not before.
As for why things stopped at low "A" for everybody but Bösendorfer, it's because of the hard limitations of the physics of the materials and the technologies that have been invented. None of this has substantially changed since about the 1870s. Physics is physics. The low "A" was the lowest note that was technologically feasible. It sounded good, and the piano-buying public was willing to pay for it. It hit the "sweet spot" between technology and commerce. Only one company in 125 years, Bösendorfer, was willing to go lower than that. Every other piano manufacturer found it unfeasible and commercially non-viable, and they still do to this day.