Just curious, what are the practical applications of a low power HF radios.  All I can really come up with is backpack rigs that can operate on very small batteries to communicate with low power/week signal modes.

Do you mean QRP? (low power, typically 5 watts)

They're for portable operation and/or for folks who like a challenge.

You mean "QRP".

Low power focused rigs are sort of two-fold:

1. Using as little power as possible means you save power resources, which are usually bulky.  When operating remote portable such as backpacking or mountainclimbing (SOTA) type activities, energy storage devices tend to take up large amounts of space and weight, so having a low power radio means you need less power reserve to keep it running.  The radio itself can also be made smaller/lighter, as the components and chassis don't need to be made to handle as much current.

2. The challenge of making contacts on as little power as possible.  To some, this aspect of the hobby adds a handicap that can make it more difficult, and in a way more rewarding.

Kinda like doing the 1 moa all day with a snub nose revolver.  

QRP radios can be made of smaller lighter weight components.

Their antennas can be thinner wire, smaller balun.

Generally people use these radios for CW or Morse code, because the narrow bandwidth required for cw means 5 watts can push that signal around the world.

Not really a challenge if  you use digital modes.  I send emails everyday, and chat on JS8Call with 5 watts.

QRP radios generally draw very low amps- are light and portable.
With a wire up in the trees with 5 watts I have had SSB qso’s around the world.

For CW  and digital they are great.

Just another tool in the box for whatever interests you.

I have a Yeasu 897D that was meant to run on batteries.
It will still run on a low battery a lot longer then most HF rigs that will cut out once they drop below a certain voltage.

My favorite-
GOAT
Rooster and Peanut.

https://m.youtube.com/user/goathiker

It's a very cool part of the hobby. I live vicariously through them by turning my HF rig down to 5 watts and seeing what can be done, which is not much on phone, though I have been known to make QSO Party stations work a bit. Yeah, I know it's not the same, need to go portable. Thinking of the 817ND again.