Perhaps it is not guilt but the pain that comes when a man loses full time involvement in the life of his children. Many men , when they have children, expect to be present 24/7 in the life of their children as they grow up. For many that view is part and parcel of the view that they had of themselves as a father. I suspect when that is no longer their reality, they feel a sense of loss and failure.
I do not think that they are trying to buy the love or presence of their children , but it is more a reaction to their sense of separation from the children for whom their plan was to be a 24/7 presence in the life of those children.
Guilt and shame are not always bad feelings; sometimes those are the feelings that stop us from repeating our mistakes.
Men are typically the ones to leave the family home , and rarely do they take their children with them. Ironically, in many states, the law would not become involved in a situation where pre custody decision a father when leaving the home decides to take his children with him , and yet few man care enough to take their kids with them. They may rant and rave about how bad or toxic the ex might be, but they never think that the situation is so bad that they should take their children with them as they leave that " toxic situation. Toxicity may be bad for them , but it is reasonable to them to leave their children in the care of a toxic person.
Most women take their children when they leave a bad or toxic situation and as such do not have the same feeling of shame and failure as a parent.
One can hardly blame a man for wanting to make the most of the time that he has with his children and to try to cram as much into that limited time.
I don't wonder so much why men act the way that they do as I find it baffling why women try to change the men who feel or act differently than the women find acceptable. It is far easier to say that our views of parenting are not compatible, and we should look for more compatible mates and partners.
It is a lot less stressful to find a compatible partner than to try to mold a incompatible partner into your particular view of an acceptable parent.