I've never been asked for "the why" before so I took some time to sort through my thoughts, the history around it. Below is what I was able to discern.
High level summary:
The desire to wear waistcoats sans jacket came from the desire to wear something to cover braces that I also feel I can knock around in. Also, to not feel committed to wearing a sport coat every time I put on a dress shirt. See detailed thought process for more.
Detailed thought process (if you are so inclined):
The high level summary may make it sound like I worked backwards from wearing a jacket but it developed from the ground up.
1st commitment: braces for high rise trousers
I've come to especially appreciate braces in that they hold trousers at the same height all day (in the pre-braces era it was frustrating to have my aesthetic ruined unbeknownst to me by gravity). With my trousers all having a 12" rise they also don't drape nearly as well without braces. Thus I committed myself to wearing braces almost anytime I dress up.
2nd commitment: something to cover the braces
Wearing braces all the time means I probably shouldn't just wear trousers and a shirt. So what to wear over the shirt? A sweater, waistcoat, or jacket came to mind. Thus I committed myself to wearing something over my dress shirts almost anytime I dress up.
3rd commitment: something I can knock around in
I don't usually feel like I can knock around in a sport coat while that is not the case with a waistcoat. For example, if I am going to recline on my sofa to read I have no hesitations in wearing a waistcoat, but I would likely take off a jacket before doing so. In addition, I didn't want to commit myself to putting on a sport coat every time I put on a dress shirt. Thus I committed myself to wearing a waistcoat instead. I do have a few sweaters as well but since sweaters are only available in a handful of colors/fabrics, they seemed too limiting as a "go to".
With all that said, I may put on a jacket from time to time but it will be the exception. If I put one on over a waistcoat that was designed to be worn without one, I accept it will look slightly off recognizing that this scenario will be in the vast minority.
Permanent style has a few articles that cover waistcoats, including wearing them on their own. The links to the ones I've read the most are below. To be clear, not all the arguments Simon makes are my own arguments but he provides perspective.
The logical waistcoat theory (part one) - Permanent Style
The Logical Waistcoat Theory (part two) - Permanent Style
Harris Tweed waistcoat, Richard James - Permanent Style
Generally, the silk backs of waistcoats today precludes them from being worn sans jacket but with a tailor, that is easy enough to overcome. As a plus, MTM/bespoke waistcoats are relatively inexpensive.
I hope this sharing has proved insightful and I welcome any thoughts on it.