Yes!

Hoarding is bad when it's costly, due to space, time, or money.

Digital media hoarding is thus not bad at all!

You have to define "cost". I have a "server" with 3 external drives connected. One is "media" and 2 are for backups. I have a drawer with 11 external HD drives which I haven't used in years that used to be my "media" and backup drives. Each of those represent money (buying the drive) and time (copying stuff from old 1TB drives to 2TB drives to 4TB drives) etc....

So there is a cost to digital media hording.

I wanted to save the videos I'd captured from my car's cameras but there's ~250gb every 3-4 months or so which is a more money needed. Plus, if I wanted them actually available to access I'd need a way to plug in more drives live into my server so more $$$$ and I'd need to back them up for when the drives fail so more $$$$.

So yea, there is a cost to digital media hording.

The storage is cheap. The cost is keeping it online and the opportunity cost of gathering, maintaining, and preserving collections.

There is a cost, but it is a much lower cost. There are degrees of hording too - saving all the video from your cars cameras permanently is pretty extreme. It would also be a lot more expensive and difficult if you were saving it to videotape.