It's my understanding, that the reason why arcade boards were so much more powerful was because they were a lot more complex thus much more expensive to design, source components and produce in large scale.
More colors, background layers and sprites with slow CPUs and graphics chips in the 80s usually meant having several RAM chips to have multiple memory buses and parallel accesses to video memory and more video memory in KB.
That's why arcade boards were usually very large and with a lot more components when compared to home computers and home video game consoles.
Sprite scaling was added to Sega's 16-bit console with the Mega CD, it probably wasn't included with the original console so Sega could beat the competition and launch it at a competitive price in 1988 before Nintendo could launch its 16-bit console.
All of this, plus an arcade machine was specialised. BomberMan needs 39 sprites?[1] Build the hardware to do that! Super Racer needs 3D polygonal graphics? Add a hardware scanline rasterizer. To put all these tricks into a home computer, though, would have made it cost many times as much as an arcade cabinet.
The hardware budget for an arcade machine could be higher because the economics are to sell a relatively small number of units at relatively high unit cost. On the other hand the hardware development budget was more limited than for consumer home computers or consoles, as that is spread over only the small number of units.
The effect is arcade machines almost never had custom chips, but often had duck-taped-together designs that threw in extra chips to accomplish tasks.
Contrast to a machine like the Commodore 64 or Nintendo which had custom sound and graphic chips but where the overall chip count and unit cost was ruthlessly controlled.
More colors, background layers and sprites with slow CPUs and graphics chips in the 80s usually meant having several RAM chips to have multiple memory buses and parallel accesses to video memory and more video memory in KB. That's why arcade boards were usually very large and with a lot more components when compared to home computers and home video game consoles.
Sprite scaling was added to Sega's 16-bit console with the Mega CD, it probably wasn't included with the original console so Sega could beat the competition and launch it at a competitive price in 1988 before Nintendo could launch its 16-bit console.