The Speccie is only popular because it was the first computer people had as a kid.
Oh and admittedly a cheap machine with relatively dumb hardware and a relatively fast CPU meant that a lot of innovative games came out on it.
I had an Atari 400 and then an 800xl back in the day. The 6502 made it pretty hard to use non hardware sprites and scrolling. And games that did use the hardware tended to look a bit samey. One notable exception was Donkey Kong which used a hardware sprite for the player and XOR based software sprites for the barrels.
Meanwhile on the Spectrum everything was done on software. And there were some heroic optimisation attempts to get a lot of onscreen action.
Colors sucked on the Spectrum though - you could only have one foreground and one background color per 8x8 cell and the colors were R1G1B1 - i.e. red, green, blue, cyan, magenta, yellow, white and black. The Atari had a weird scheme where you had 16 colours each in 16 luminances.
And you could do all sorts of weird overlays of hardware sprites, called players, and the background, called a playfield. And you could also switch video modes each scanline.
Still a lot of Atari games used a couple of players on a rather low res but 4 color playfield which looked very generic. On the Spectrum if you ignored color you could do some pretty impressive bitmap based graphic animation in software.
Basically the Ataris were expensive machines with very clever graphics hardware but a rather slow CPU - witness Landon Dyer's comment that 'mask and paint' with four software sprites was 'way too slow'. The Spectrum was a cheap machine with very dumb graphics hardware but a CPU which was fast enough to do clever stuff in software. It's sort of like CISC vs RISC.