First off, I think you’re completely right in that laptop batteries are definitely a non-ideal solution. And, I’m really not an expert in this, so take my words with a grain of salt.

You could mitigate a bit of the dangers by doing some of the following (I only did the first):

• Reducing the max charge level to 50% of the capacity.
• Monitor your batteries health to alert for any discrepancies.
• Switch out your batteries every couple of years (which is super easy without downtime on the aformentioned old thinkpads).

If you are an under $100 budget, there seems to be an argument that maybe you are willing to risk a little bit for that extra power reliability.