Maybe I'm just internally resistant to appearing weak in interactions. I find that this never works for me. I always come off as patronizing and condescending, even when that is not my intention in any way. For me, at least, just being somewhat minimally competent and trying to self-service, then making that competence known and clear at the first contact seems to have the highest success rate.
I think what method works best really depends on your personality type. I agree that the goal is to ensure that you are making the interaction smooth by get the person you're asking for help what they need. But I also see asking for help as two different modes.
1. I'm asking for help because I am not empowered (access controls, specialty tools) to fix my own issue, but if I had been so empowered I could have resolved it on my own easily.
2. I'm asking for help because I don't know the solution, but I'm competent enough to narrow it to a particular trouble area.
In #2, I acknowledge outright, internally and externally, that because I am asking for help I have reached the limit of my competence. My request is inherently respectful, because I'm acknowledging the superior competence of the person(s) I'm asking for help from, but out of respect for their time I do my best to ask a good question and provide all the necessary details to make helping me a low friction event.
In the case of #1... often it's better to aggressively establish your own competence to get them to just do what you need done. Unfortunately in the world of large organizations and bureaucracy you will deal with a lot of incompetent people who are put in a position of some tiny fraction of power over you. You need to get them to exercise that power to your benefit, but you also need to not alienate them so they withhold it. People with only a small amount of power can be extraordinarily vindictive, so it's best to approach them with a measure of respect, but also clearly establish the boundaries of the interaction so you can proceed as quickly as possible and be on with your life.
I've worked roles in which I was in both situations on the other side of the table, but I had enough self-awareness to realize when I was the monkey in #1 and I did my best to be as efficient as possible and let people get on with it. In situation #2, I understand very deeply the frustration of having someone essentially toss something over the wall and in so doing show their disrespect for your competence and the value of your time. As always, you want to go through life without making other people feel badly, but taking a submissive pathway will not always work for you, especially if that is not in your nature.