The trouble with your theory is that it ignores the fact that Cohen will pay and pay big if he lies here. He has only motivation to be truthful, he's hoping for a further sentence reduction for cooperation. Anything he gives, must be corroberated, due to credibility, but if he gets through all of this successfully, even if you don't see or understand it, this is very bad for the president any way it's looked at.
For the Democrats to actually get Trump with this, impeaching him, the need to get a lot right, no telling if they will or not. The trouble is, this is damage to the president that will sloly grow, it is not going away. It will make him unelectable, if he already isn't. The Democrats would obviously need help in the Senate, but this is a time bomb. As it goes on, more and more damage to the GOP< and the Senate won't be able to ignore it forever.
I cannot figure the GOPs motive for protecting the president, and I know that many of them privartely, do understand the damage they're doing to their party by continuing to support him. The celebrity reality TV show appeal can't be woth the long term damge.
Both parties can and may really blow it over this president. The fact remains, their just isn't any motive for lies here, and corroboration, is necessary for credibility, but politically or criminally, this is damaging the president, and the damage will only grow. The Democrats would have to grossly overreach to even possibly make the president re-electable. Not impossible, but at this point, they have shown no sign of that.
Donald Trump's big mistake was not dropping out from the primaries. I have no personal doubt, he regrets it greatly now. He doesn't even want to be re-elected. I'm not sure how his fans don't see that.