Given that the US Justice Department's policy is that a sitting president cannot be indicted for a crime, and the Justice Department seems to be acting as Trump's personal representation, I don't see how that would have changed anything.
Of course, the Justice Department's policy is based primarily on the fact that the remedy to "indict" a sitting president is impeachment; and this takes us back to the "does there need to be a crime" loop of argument.
I subjectively happen to think quite a few Americans, and then perhaps their representatives, would have been more open minded if the charge wasn't so nebulously and politically drafted. Or, as someone else put it, if the House called a turd a turd.
To just one specific note, "abuse of power" has no mens rea requirement. A lot of Democrats talked about wanting to know Trump's motives, but abuse of power is not a crime. Thus there is no mens rea requirement necessary to prove "abuse of power," whatever that is. Thus there really is no evidentiary need to determine Trump's motive -- it's not necessary to prove the offense.
Conversely, 18 USC 201 (the federal bribery statute for public officials) does have specific intent requirements. Thus making intent extremely relevant. Thus making calling certain witnesses far more necessary. Thus improving Democrats' argument about the issue. On and on.
But if the charge is just "abuse of power," that's a completely subjective interpretation with no case law, no statute to follow, no mens rea requirement, etc. It's just a nebulous cop-out to me.
I think the House would have been better off calling a turd a turd.
This sounds like a plausible explanation to me.
Bribery, defined as soliciting a favor or benefit in exchange for influencing an official act, seems to fit Trump’s conduct: He asked for announcements of investigations in exchange for military aid and a White House visit.
But rather than trying to satisfy technical statutory requirements such as “quid pro quo,” and allowing Republicans to quibble over legal definitions and factual conclusions as to whether one thing was conditioned on the other, House members would be wise to frame the articles more broadly in terms of abuse of office—which is at the heart of impeachable conduct. The law professors testified that the greatest fears of the framers were foreign influence, subverting elections, and abuse of power to promote personal interests. Here, drafters could make a compelling case that Trump’s conduct has made all of those fears come true.
My take on it is that a reasonable person can look at the relevant facts and say Trump was not asking for the investigation because he wanted to investigate corruption. The timing and justification just don't add up.
However, House Democrats knew that the jury would not be made up of people using basic reasoning skills, it would be made up of senators with a stake in the outcome of the trial. Therefore there would be nothing stopping them from arguing that Trump's motives were, if not entirely pure, at least mixed. As in, he sought the investigation for personal gain but also because he wanted to go after corruption.
If his motives were mixed, charging him with bribery would set bad precedent as it is very common for politicians to have mixed motivations as is quid pro quo. When you mix those two elements, most politicians could then be charged with bribery. For example: representative Bob agrees to vote for X in exchange for funds for a new school. There is quid pro quo, but it's not for personal gain so it's all good. But wait, if Bob gains favor from voters because he provided a new school, it is for personal gain. Now there's mixed motivation.
So again, I don't think that's an honest argument unless you believe Trump really wanted to go after corruption, but it's an easy enough argument for Republican senators to make and never admit that Trump did anything wrong.
Instead they charged him with abuse of power which basically says, "We all know what happened here, do you really think this is OK?" and in the end some senators admitted, "this was not OK, but I'm voting to acquit anyway"
This doesn't explain why they didn't include bribery as a third article. Perhaps they didn't want to give the Republicans a reasonable argument to latch onto and give them momentum in the media?
In any case I don't think House Democrats ever believed he would be removed, so the real goal was to influence public opinion. If Republicans could give technical reasons for why they voted to acquit, then even those who dislike Trump might agree with their vote.