I will politely say, you have no clue whatsoever.
You seem to think annulment means "erasing" a marriage. It doesn't. I'm not going to explain it, you can/would find out for yourself if you were truly interested.
The Church makes the annulment process anything but easy.
The cost also is not much, considering a tribunal spends months or years on a case. And, if one can't afford it, it can be "dealt with".
You sound like alot of people who like to make sweeping pronouncements about the Church, when they really don't know much beyond rumors and talltales.
An annulment means that in the eyes of the Church, no marriage ever existed. The couple were never married. That sounds remarkable like "erasing" a marriage. The children are "legitimate" from a civil legal standpoint since they were the children of a legal marriage, but they were not the children of a valid Catholic marriage in the eyes of the Church, and in the eyes of God, according to the judgment of the marriage tribunal.
No, that's not it.
I saw a couple go through hell getting one in the 1980s, and he had a child from a first marriage.
It was sad.