The thing I dislike most about the term "white privilege" is the implication that it's a privilege to avoid having various bad-to-horrible things happen to you. This is related but not exactly the same as your point #2, which I also agree with.
In particular, we already had perfectly good phrases to describe the more serious problems: racial discrimination, institutional racism. If people aren't looking at your job application because you're black, that's not meaningfully because the other people have "white privilege"...no, it's because they are (perhaps implicitly) racially discriminating against you. "White privilege" absolves individuals of their culpability in maintaining unjust attitudes, behaviors, and thoughts, placing the whole burden on society instead. This is ridiculous!
I don't think we need new words yet. I think we need to use our old words properly. No delicately avoiding the actual issues with some vague reference to "white privilege".
Fix hiring practices to decrease racial bias in hiring, and practices around promotion and retention to decrease racial bias in those areas. (We know how to make huge impacts in this area. We just need to do it.)
Fix the criminal justice system, including propensity to use violence, lengthy imprisonments awaiting trial, the classist bail system, the poor quality of public defenders, the increased rates of hostile interventions, etc. etc..
Fix the other instances of just flat-out racial discrimination, whether subtle or blatant.
Then, let's see what's left. Is it even worth talking about that much? Maybe the funding for skin cancer will disproportionately benefit white people, because on a national level it's a significant problem by virtue of how many light-skinned people there are. I think we can survive the little disparities like this, once the big things are fixed.
Most of what counts as "white privilege" is actually "just having your basic rights respected by individuals and institutions in your society". This isn't some elitist thing that only a few can aspire to, as the word "privilege" suggests. This is basic stuff that everyone should expect.