If you interpret these sayings as “just wait around without doing anything and the problem will fix itself”, then you’re missing the point. The point is that everything is always changing, and that includes the situations in our lives and how we feel about them.
When you’re at the bottom of a slump, it often feels like it’s going to stay that way forever. But this feeling is an objectively false view of reality. Reminding yourself that “this too shall pass” can help to cut back on the despair and allow you to focus on taking steps to prepare/help the healing process rather than just giving up because right now it seems like it’s pointless, life is suffering, God is a lie but the Devil is real, and everything will suck more and more forever.
I feel likes these sayings are more of a commentary om how one needs to accept certain things in life and learn to move past them.
For Achilles, time wounds all heels.
When I started training jujitsu it was in an old YMCA, and we had to lay out the mats before each class, and put them away afterwards. The mats didn’t fit the floor, and didn’t have that puzzle piece shape, so they would slide around a bit. And sometimes there would be a gap between the mats, so Sensei cautioned us to be aware, lest time wound all heels.