Makes sense, that's a quick and easy solution.
One thing you could still play with is using different levels for different types of assets - especially compressing backgrounds with lots of details and noise with lossy WebP will provide a *massive* size improvements compared to PNG which is terrible at compressing that (as showcased in my example of 2.4 -> 0.6/0.2), which could allow you to still use lossless for the sprites. Kinda best of both worlds.
But mostly, I just wanted to make sure you knew that lossless is an option for you to use :)