After posting this question, another one, more obvious came to mind.
If the "first sale doctrine" is a widespread law, and allows someone to give their whole collection of VHS or DVDs or vinyls for free, then why is this rule not applying when it comes to a digital copy?
If the first sale doctrine rule applied, then someone who legally purchased thousands of albums and movies digitally should be able to give these files for free to whoever they want.
A frequent distinction between the two situations is that usually, you buy the actual physical thing (DVD, VHS, CD, book, etc.), but for a purely digital asset, you may be only buying a restricted licence to the asset (on iTunes, for example).
In the case where you did buy the digital asset (not simply a restricted licence to it), another difference is that the transfer of a physical item does not implicate the reproduction right1 that is given exclusively to copyright owners. However, transfer of a digital asset often does implicate that reproduction right. See Capitol Records, LLC v. ReDigi Inc.:
It is also undisputed that Capitol did not approve the reproduction or distribution of its copyrighted recordings on ReDigi’s website. Thus, if digital music files are “reproduce[d]” and “distribute[d]” on ReDigi’s website within the meaning of the Copyright Act, Capitol’s copyrights have been infringed.
It is a different situation if you transfer the actual medium onto which you downloaded the digital content (ibid.):
Section 109(a) still protects a lawful owner’s sale of her “particular” phonorecord, be it a computer hard disk, iPod, or other memory device onto which the file was originally downloaded.
1. 17 USC §106 (1) "the owner of copyright under this title has the exclusive rights to [...] reproduce the copyrighted work..."
This answer assumes US jurisdiction, but Canada's Copyright Act is fairly similar to 17 USC and similar holdings have been made in Canada.
The first sale doctrine only applies to materials you own. If you bought and own the digital copy you can give it away or sell it provided you delete your copy - remember copyright prohibits making copies.
However, many works, particularly digital works are licensed, not sold. If you have possession through a license then you do not own the item and the first sale doctrine does not apply.
