34 minutes ago, drpaladin said:

For some reason inveterate seems to always be paired with undesirable habits and behaviors.

My thought exactly. As in inveterate liar. It seems to carry an implication, or connotation, that the "particular habit, activity, or interest" is a vice.

Just the facts:

Inveterate Definition & Meaning - Merriam-Webster

A person could be an inveterate reader, and I don't think any of us here would look at that as being a negative characteristic.  

They might also be an inveterate coin or stamp collector.  Or an inveterate TV watcher (I believe this one may depend on your point of view if it's a negative quality). 

My inveterate procrastination is often accompanied by twenty-five open tabs and I have no idea where the music is coming from.

11 minutes ago, JamesSavik said:

My inveterate procrastination is often accompanied by twenty-five open tabs and I have no idea where the music is coming from.

 Possibly it's just in your head.  

19 hours ago, Bill W said:

A person could be an inveterate reader, and I don't think any of us here would look at that as being a negative characteristic.  

They might also be an inveterate coin or stamp collector.  Or an inveterate TV watcher (I believe this one may depend on your point of view if it's a negative quality). 

I agree and I could also say a person is an inveterate lover, which their partner views as very positive. Humorously I could refer to someone who has been married a few times as being an inveterate serial monogamist without being critical even if their various spouses have differing views.

My point is simply that words are both denotative (dictionary meaning) and connotative (emotional response). Inveterate is predominately used with a negative connotative implication and very rarely with a positive connotative implication.