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.