Is PDF very inefficient?
Not particularly, as your comment to the Q shows:
'cos the PDF of 10 greyscale pics, is 6.35MB!
It all depends on the resoution and level of compression.
Fundamentally the answer is: full pages are quite large and typical scanning and printing resolutions are quite high: thus lots of data.
A4 is about 8.3x11.7 inches (letter is similar, different is not significant). So one page is 97in2.
At 300dpi, 1in2 is 90,000 pixels. At 24 bits per pixel (enough for 16 million colours) that’s about 260kB.
So 100in2 will require about 26MB. This matches your figures. NB greyscale at 8 bits per pixel (256 levels) requires about a third of this.
The 1GB Of Intermediate Files
But if you want a final output of 300dpi you really need to work a higher resolution until the final output stage (to avoid artefacts: just try opening and saving anew a JPEG with even moderate compression a few times to see how these quickly appear).
My old scanner (>8 years old?) would operate at 2400dpi (IIRC), so something like 600dpi would be in easy range of most scanners, since that is the linear measurement, the per-area—and thus file size—will increase with the square, leading to file sizes four times bigger.
I.e. ∼100MB per image, so 1GB for 10 is to be expected.
But the final output is much smaller
This is almost certainly compressed. Non-loosy compression of images with large areas of constant colour can often be compressed by x10 with no significant loss of perceived information, for scans and photos (which tend to have a lot of small amounts of variation that we only see at extreme zoom levels) some loss is normal (as JPEG uses) and similar compression ratios are achieved.
How Big Could It Be?
Pro-DSLRs use 14bits per colour (a high end scanner should also be able to), i.e. 42bits per pixel. Scanning A4 at 4800dpi would lead to a raw data size of ∼11GB for a single page.