I'm not that much into printing, but I did print some family snapshots over the past few years, using a hybrid process: shoot - develop film - scan - print the digital file onto paper using a local photo lab.
I scanned the same frame (Fomapan 100 in D76 1:1) both in an Epson flatbed (V550, same as the V600 hardware-wise, so perhaps around 1800 dpi) and in a dedicated film scanner (Minolta Scan Dual IV, about 3200 real dpi). The lab was instructed to produce exactly the same print (all 'auto' postprocessing was deactivated) from the two 16bit grayscale .tif files.
The difference across the 2 20cmx30cm prints was immediately noticeable. The print from the dedicated film scanner was vastly better.
So it's not a matter of pixel-peeping onto a computer screen only - although that's important for some people, too.
The differences are visible in a moderate size consumer-level print. Those of you who print at a much higher level of quality than I did, and use much more resolving film, will agree the scanning has a tangible impact on your prints, at least, in my experience, if you start from a 35mm negative and aim to produce something around an A4/letter sized print at least.