Well I can tell that in at least one case the only painful part was writing out a $7,000 check to the church. She said at one point how easy it was.
I don't recall the specific book, but the Bible warns that those who sin because of others in authority will be punished, but that those in authority will be punished even more. I've always thought that this would apply in cases of annulments being granted when they shouldn't be. So if a person has a weak case, but the committee is overly "pastoral" and decides to grant it, then if the person accepts their incorrect decision in good faith and remarries, they really are only partially at fault.
It would seem to me that if the person is rolling the dice rather than truly believing they have a good case, and they are surprised if the committee decides in their favor (perhaps even believing that the donation played a part in it), then if the decision was wrong, and the person even thinks so, then the remarriage would be a serious sin on the part of the person.
I'm not sure if I'm being clear but if it shouldn't have been annulled, they will have to answer to Jesus about it. You can't lie to God. This is all very important in terms of salvation.
In my diocese, the (significant) costs are underwritten by our annual diocesan donations which is why I tend to give more. The costs of the canon lawyers, other salaries, etc are not minor. Having fees in the neighborhood of 5-10K give the impression of buying an annulment and thus should be avoided. I think if you can't afford the $175 due to hardship, it can be waived. The first step in an annulment in our diocese (not sure if it's the same everywhere) is filling out a 90+ question document some of which requires serious soul searching. MANY people give up one they read the different requirements for a finding of an invalid marriage or when confronted with the questionnaire.
The only thing that could be considered easy is one granted to Lack of Form, basically if a Catholic marries outside of the Church without permission. This is mainly for those who leave the faith, perhaps becoming a Lutheran or Baptist, marries, divorces and returns to the Church. Then it's just a matter of legal documents, witness statements and a small paperwork fee (certainly not 7k!!).