This is not a welfare issue. It's about planning. Welfare isn't like a savings account that a woman can fall back on because her husband failed to provide for her if he passed on. It's a step up, and should and can be used for such. I know of situations first hand in which it has been so.
I also disagree that today's society makes it harder for women who have lost their husbands. Things have not changed that much. It has always been hard on women when left alone with children. In colonial America children were oftentimes forced into indentures. In merry old England they were sent to poorhouses. Women throughout the centuries have married after being widowed because they had little or no choice in order to survive. The weak and vulnerable, which are women and children, are always at risk in such situations. Not everyone had parents, in-laws, or a farm to retreat to. Indeed, women and children cannot work a farm and were merely more mouths to feed. No one really wished to have them along.
The "something to fall back on theory" is also not fool proof. If a woman never uses that degree, it becomes bankrupt about the time she is 30 depending on the field she is in. Even if she did work with that degree for a time, if she does not for a number of years it can become difficult to access it and use it by the time she is nearing 40. Of course, some degrees are better than others - nursing allows part-time hours, accounting part-time on-the-side work, some other degrees do as well, so that she can work part-time and keep up her skills. But when a women is knee-deep in diapers with three children under the age of 5 needing her care, or homeschooling six or more kiddos, she does not have time to worry about keeping up her degree skills. She just wants sleep and to go the bathroom without someone calling for her.
And a woman working does not ensure her survival if her husband does die. If their debts are high, or they have a lot fo loans, etc., she will still have a hard time after he is gone. She has learned to live on twice the money and now has to live on half of that.