Third party inference costs are a moot point for people running these models locally.
I am currently serving Minimax M2.7 to myself at ~$0.015/1M blended tokens worth of electricity on my own local hardware, where I get all of the confidentiality, integrity, and availability benefits that are lost when choosing to run open weight models on someone else's API.
Open source means that all of the information necessary to recreate the final product is public, which in the context of LLMs, would include all of the training material, and build instructions (scripts to do the training). Very few models actually achieve this - Nemotron family is the only one that comes top of mind. A license to run, inspect, modify, and re-release is a good improvement on open weight models, but does not alone amount to the model actually being open source.
You are welcome to an alternative understanding of the definition of open source - as you correctly note, it's a contested term - just know that your definition is not the more widely accepted one that people think of when they hear "open source".
Your version of the term is much more aligned with the OSI, which was a federation of anti-FLOSS industry bodies created with the intent to capture, redefine, and weaken the original spirit of the FLOSS movement, which predates the OSI by almost a decade - the GPL was first released in '89, compared to the OSI's formation in '98 by members of the $10B for-profit Netscape Corporation, who's flasgship product was originally proprietary and was only open sourced after commercial failure against proprietary competitors.
None of this should be construed as an implication that I'm anti-open-weight. As I mentioned earlier, I think open weight models fulfill a lot of the spirit of open source. While a world where truly open source models are the norm is obviously preferable to a world where only open weight models are the norm, a world where only open weight models are the norm is still vastly preferable to a world where proprietary models running on other people's hardware is the norm.
I just think that we should be careful to avoid watering down terminology in ways that serve proprietary commercial interests over the interests of the public and of users. Open-washing is real, and it harms the intersts of users.