You are correct. Annulments are not guaranteed!
Nor should they be. We have to be open to the fact that they may be denied, not because of bureaucracy and insensitivity, but because of love. For that matter, we also have to be aware of the dangers that bureaucracy or social pressure can sometimes push through annullments that erase marriages that really were valid; annullments that hurt people.
The media has redefined the process in the minds of most people, so when they see “annullment granted” they feel this is a result of compassion, and when “annullment denied”, this is a result of bureaucracy, rigidity, inefficiency, and general heartlessness.
My diocese has “annullment companions”. They do annullment workshops, they coach people on writing or saying what will help “make the annullment happen”. They may even send someone to another diocese, if the ex lives there now, depending on their political (not spiritual) discernment of the “process”.
I never hear about advocates, or “companions”, trying to help struggling persons save their marriage, or live chastely after a marriage ends. The children may be offered counseling to deal with the certainty of issues they will have, but no one advocates for them, as adversely affected by remarriage(s).
The younger sister of the person who has gotten annullments is affected by this, when she marries for the first time. It influences how she shapes her own marriage, in terms of provisional or permanent.
A protection is being withdrawn here.