There were economic reasons, but they were not about getting to amateur market; it was more like getting any market. The main merit seen in early digital photography was speed of delivery (no need to develop films), so news agencies were the first targets.
During the dawn of digital photography, a full frame sensor would have been enormously expensive to produce. The technology was just not ready to produce perfect silicon wafers of that size; even the smaller ones were the price of a really nice car (or a top-notch medium / large format system). The first commercially available dSLR, Kodak DCS (1991, a.k.a. DCS100), managed to sell 987 units (with 1.3MP 1.8 crop factor sensors, some of them monochrome) priced at $20k...$25k (almost a median US household income). Provided that most professional photographers were convinced (and correct) that digital image quality was significantly worse than film, the market would have been too small for full frame cameras at their enormous price.
The first FF dSLR, 6MP Contax N Digital, came 11 years later at $7000, a sixth of average US household income. 11MP Canon 1Ds was announced at $8k the same year.
Smaller sensors were (and still are) several times cheaper, and with the 1.5 or 1.6 crop factor, the quality difference was (and still is) not that big to justify the cost difference for most people. At the same time with 1Ds, APS-C Canon 10D was announced at only $2k.