But since you know you already have a fairly powerful computer that's doing the printing, it seems much more logical to me to rely on that computer to do the heavy lifting and bake everything down to bitmap image which the printer draws on the page. And that would make printers much cheaper, by requiring them to have less CPU smarts and RAM than if they need to run complex Postscript programs.
Well, the thing is, when Postscript debuted you couldn't necessarily rely on the computer being powerful enough to rasterize complex documents. (Or even have enough RAM to hold the resulting bitmap.) While PostScript proper is sort of an unauthorized clone of Xerox's InterPress system, which included one of the first WYSIWYG text editors, the concept of a "page description language" to drive automated typesetting dates back to at least the early 1960's. (IBM's SCRIPT, TROFF, TeX/LaTex...) Originally these markup languages (which can be thought of as direct ancestors to things like XML and HTML) were used to drive phototypesetters that used optical "font disks" to create photographic negatives that were turned into metal offset printing plates but it was a very natural transition to go from that to digital rasterization-based systems driving Xerographic print engines when the technology caught up. A pretty brain-dead eight or 16 bit computer was sufficient to generate typeset pages using these markup languages so the ability to do it on your desktop even minus the WYSIWYG was a pretty big deal.
(WYSIWYG actually buys you very little if you want to use the system to generate documents automatically. Once you have the template you don't need much of a computer to accept the text streams from whatever sources and fit them into it.)
And, while less of an issue, the bandwidth limitations of the communication channels could actually be a problem. Localtalk, which is roughly middle-of-the-road in terms of speed of early 1980's printer interface ports, runs at around 30k a second so spitting out a letter size page at 300dpi will take a bit north of 30 seconds not counting rendering time. Might be able to subtract some if the bitmap is compressible. For mostly-text documents a Postscript printer with a fast engine could seriously outrun a printer that had to have bitmaps spoon-fed to it. (Most of the really early "dumb" lasers used something other than a normal printer port because of the speed limitations. Apple's early entry used SCSI, while Atari and NeXT used high-speed DMA ports.)