No, it's not natural. In your example, you'd use a word like 'understand' instead of 'digest'. 'digest' has broader use in more formal writing as in journals. But in conversation, the usage is far narrower. Usually it's reserved for when you are talking about meals or food. An example: "I ate too much at lunch and my stomach's having a bit of trouble digesting it". Yes, you *can* use digest a little broader in conversation in some instances ...'He had trouble digesting the news', etc. But not many people will say it this way, so it's very uncommon to hear it.

It's correct, but not so natural. "digest" does not generally mean "understand", but more like "live with", "accept". It suggest a reaction as if you had eaten food that you cannot digest. Hence not followed by "why" I cannot accept that we have to carry such ... I digest having to to carry such ...

Sure. I can't figure out why we have to .... I can't figure out why we should be ...