To be concrete, if you have a 256×192 screen divided into 32×24 tiles of 8×8 pels (as the Spectrum ZX did) the biggest full circle you can draw is 192 pixels tall. It only has 74 distinct tiles, counting "all filled" and "all empty" as distinct tiles, and if you can mirror those horizontally and vertically (as the Atari 2600 did for its backgrounds) you can make do with 20.
I think a very reasonable balance would have been a pattern table of 256 distinct 8×8 tiles with 2 bits per pixel, totaling 4096 bytes of RAM; a tilemap of 1024 8-bit tile indices and 1024 16-bit tile attribute words, including three 4-bit colors and two mirroring flags (and two spare bits), totaling another 3072 bytes; and 2–8 sprites of 8×8 or 16×16, also 2 bits per pixel, totaling maybe 256 more bytes. This would have given you spectacular, NES-quality sprite and tilemap graphics, but with enough flexibility to do the 3-D isometric graphics in the Spectrum's most spectacular games. And it would have left you a lot more space for game logic. (Maybe you could have stolen a bit from the tile attribute word to get 512 pattern table entries, nearly as many as the 768 tile positions on the screen.)
Could the gate array in the Spectrum have done it? Maybe. Let's say each of the 192 logical pixel lines gets scanned out three times. On 576 out of 625 PAL lines, 50 times a second, you have to spew out those 256 pixels in PAL's 51.95 μs, a dot clock of 4.928 MHz, 203 ns per pixel. (So far, this is exactly what the Spectrum did do.) Each 2-bit pixel value controls a 4-way mux among four colors, three loaded from the attribute word and one loaded from the background color. (Separately you have a sprite engine that's maybe doing the same thing from a sprite or two, and one pipeline stage later you mux between the background and the sprite foreground under the control of a registered bit from the sprite engine.) Every 8 pixels, 1.62 μs, you need to clock in the colors from the next attribute word—exactly as the Spectrum in fact did, but 12 bits instead of I think 6—out of the 384 bits of colors for the 32 tiles on the current row.
These are the only parts of the display driver that have to be fast: the 512 bits of the current pixel line, the 384 bits of colors, the perhaps 32 bits of pixels and 12 bits of color per sprite, and the shifting and mux logic. This is definitely more than the 256 bits of pixels and I think 192 bits of colors the Spectrum actually did have to handle at this speed, but only moderately more. And the difference in visual expressivity would have been night and day. Maybe you could even have afforded higher vertical resolution (as, again, the NES did).
There are other tasks that need to happen concurrently: every 3 scan lines (192 μs) the pixel line needs to be reloaded from the tilemap and the pattern table, a task which involves indexing into the pattern table 32 times by combining 32 bytes from the tilemap with a (possibly inverted) 3-bit line index, and possibly pixel-reversing the row loaded from the tile; this can be done either during the 64 μs of the third scan line (500 ns per index), if the 512 bits are dual-ported, or during the entire leisurely 192 μs period (1.5 μs per index), if you double-buffer them and switch back and forth between two 512-bit buffers every third scan line. And every 8 pixel lines (1536 μs), the 384 bits of color attributes need to be loaded from the attribute memory. And of course the sprite states need to be updated, which may involve loading a new sprite from RAM or just incrementing a counter or two. Because these tasks are so slow (totaling maybe 2.46 μs/byte) they can all be done by a single state machine timeshared between them, maybe driven by an EPROM.
Since the 512 bits of the current pixel line are accessed in a strictly sequential shift-register fashion, and can be reloaded during the third scan line after scanout, even the old Signetics 2503 dual 512-bit PMOS shift register chip (DIP-8 or TO-99, 10 MHz typical, 4 MHz guaranteed, available 5 years earlier) might have been adequate. But I suspect much better chips were available by 01981. The 384 bits of color attributes are also accessed in a similar sequential fashion but at a much lower rate: they just need to be loaded into the color MUX inputs in 12-bit chunks at 617 kHz.
I count 27 chips on the motherboard in the photo at https://en.wikipedia.org/wiki/ZX_Spectrum#/media/File:ZXspec..., including what I think are 16 memory chips, so adding an extra chip like the 2503 might have increased the cost by 3%.
If you could stick the pattern table off in its own 4096-byte or 8192-byte RAM area instead of sharing the bus with the CPU, it would probably make the machine a bit faster too, but I suspect that wasn't practical because you couldn't get 4-bit-wide or 8-bit-wide RAM chips yet. I guess you could have used a 1-bit-wide pattern-table RAM chip and indexed it bit-serially, especially if your 512-bit pixel buffer was double-buffered (note that the 2503 was in fact two 512-bit buffers.)
But that's all with the benefit of hindsight, and without really knowing how tiny or slow their gate array was, or what alternatives there were for memory chips, or how much they cost. Undoubtedly at the time I would have been as blind as anybody else and, if I didn't make the same mistakes Sinclair did, I would have made others that would likely have been just as bad.