The Amiga did come close-ish, but despite its custom chips, the lack of a custom sprite scaler and too low memory bandwidth would have likely made it impossible to get all that much closer (it's mainly lacking extra details next to the road). The dual 68k's on Outrun also ran on 12.5Mhz vs. ~8Mhz/7.16Mhz (depending on NTSC vs. PAL) for the Amiga's single M68k.
Outrun on Amiga: https://www.youtube.com/watch?v=eOGxxYm4z5I
Outrun on arcade: https://www.youtube.com/watch?v=J7tZFW4WedI
> Who wouldn't try to buy a machine that could play, for example, Outrun, close to the arcade? even if it cost 1000 dollars...
In effect the Amiga was the closest the market would bear - Commodore struggled on for years, and sold about 5m Amiga's, and the only reason they survived as long as they did was that Commodore were masters at cost-cutting (arguably that also sank them: they cut their R&D budgets to the bone, among many other mistakes). People who went from working at Apple to Commodore at the time have indicated that attempts at Apple to figure out how Commodore was able to sell the Amiga at the price-points they did for example massively over-estimated Commodores manufacturing costs and could not figure out how Commodore were able to squeeze out a margin at all.
As such we can assume the Amiga price, which including a monitor, joysticks etc. around the time of Outrun would easily ended up in the region of 1000 dollars or more, was the high point of what was commercially possible around the thousand dollar mark at the time.