Try to get the screen or battery replaced. To be fair, they're easier user serviceable than newer MB(A/P)s. For example, me with my MBP 2015 will have a harder time to service it once it gets EOL (hardware-wise) than you have now with your MBA 2012.
I've replaced the battery twice, last time in september 2019, and this last time it costed me 60 EUR, and the battery life is much better than the original one.
I might want to replace the battery again in the next 3-4 years if I still have this laptop, and you might be right in that this might not be possible, but at least today it is.