Of course, culpability is a matter for a confessor to decide. I do not think that is the problem though. The problem is how to deal with a presumptively valid first marriage. It was not the Church that decided that marriage was a lifetime unbreakable bond, it was Jesus. The Church cannot just decide that “well, He was wrong about this matter.”
In order to solve many of the situations in favor of a second or third marriage, there is going to have to be something pretty close to a presumption of invalidity on the part of first marriages, which is quite different from the current view, wherein the Church presumes validity unless proven otherwise.
When a whole society no longer takes marriage seriously, perhaps a presumption of invalidity might be appropriate, but that would be a significant change.
The ongoing problem is not the validity of the first marriage, it is the continuation of a life that involves objective sin. For someone abandoned, there is no mortal sin attached to the civil divorce but there is to the conjugal relationship with a new partner. Even if the first marriage was declared nul, but the couple continued to live in a conjugal relationship without having the marriage convalidated, they are still in a state of objective grave sin.
A couple who have never before been married are in exactly the same situation, they are in a continued state of objective fornication.
The difference is that the never-married cohabiting couple, or the one with a decree of nullity, can do something about it. The one who cannot get a decree of nullity, cannot.
In all these cases as long as the couple are living together in a conjugal relationship, the couple is barred from
all of the sacraments, not just communion, until either one of two things happens: they separate, or live together as brother and sister.
The solution, IMHO, is not always through the annulment of the first marriage. If it cannot be annulled because of a non-cooperative ex-spouse or other reason, the solution is to determine that the ongoing conjugal relationship, while
objectively gravely sinful, is
subjectively of venial culpability.
That is an issue of discipline, and not doctrine. Again, as these issues are complex including fault for the first marriage failure, it should be dealt with in confession, with the confessor being provided with clear guidelines. For instance a remarried woman who left an abusive husband 20 years ago, or was abandoned by him, would not be treated the same way as a man who just recently abandoned is wife to shack up with a younger woman.
What many are asking is for a chance for those caught in the first example, to rebuild their lives and have access to the sacraments. For those in the second example, you reap what you sow.