In the mishna on Sotah 7a , we learn that the beis din intimidates the sotah in order to try to get her to admit to wrongdoing and avoid drinking the sotah water. The gemara on 7b asks why our mishna doesn't mention a fact that we learn from a beraisa: that the beis din also encourages her to drink the water if she's innocent. This difficulty is resolved by saying that the latter only happens after the name of God is erased in the water and our mishna is talking about before that happens.
It seems to come out from this that before the name is erased, the beis din does not encourage her to drink the water if she's innocent. They only intimidate her and try to get her to admit to wrongdoing. So it seems that the sotah falsely admitting under coercion is considered a better outcome than going through the process and finding her innocent by drinking the water, even though it means that she becomes forbidden to her husband and loses her kesubah. Obviously this is troubling, but it also seems to undermine the entire point of the mitzvah of sotah. If erasing God's name is such a bad thing that we prefer to forbid the woman to her husband and have her lose her kesubah over erasing the name and giving her a chance at vindication, why does the mitzvah of sotah exist at all? Why not just have that be the punishment for a sotah and leave it at that?
Even if it's true that the vast majority of sotahs are guilty, they know the truth. So why couldn't the beis din do two things before erasing the name:
Intimidate her and try to convince her to admit guilt if she's guilty.
Assure her that if she's innocent the water will not hurt her.