The Onion

You are making the mistake of assuming only one thing can be done at a time, and if everyone is not focused on "the most important thing" at all times then it is inefficient. This is not only untrue, it causes nothing to progress because nobody can agree on what the "most important thing" is.

Things can be worked on in parallel. While a group works on how to best address homelessness, another group can address LGBT issues while yet another group tackles environmental protection.
You can't just throw everyone on a single problem or it becomes less efficient. Sure, 2 people can sweep the floor faster than 1 person, but if you try to get 100 people sweeping the floor in order to "prioritize it and get it done faster" it's going to be a nightmare and never get finished.

Having one person sweep the floors, another clean the windows, another do the dishes, another do the laundry, another make dinner, another wash the dog, another mow the lawn, another tidy the living room, etc. Is going to have the house clean and in shape a lot faster than if you have all those people make dinner (because dinner is the most important) and then have everyone mow the lawn, only after the lawn is finished have everyone do the laundry....

And all of this ignores the fact that I am not in government. I cannot meaningfully address the homelessness issue. I can stand up for the rights of trans people.
Maybe I could form a group to try to find the most effective methods of addressing homelessness and send our findings to the government. Okay, once we've done that now what? Government takes time, homelessness still exists, I guess we double check our research? Yup, research still looks good, our findings still stand. Guess we'll send that to the government as well. But there's still homelessness and homelessness is more important that human rights. (Sorry, trans rights. Trans rights are less important because there are less of them and neither you nor I are trans.) So seeing as homelessness still exists and is more important I guess we triple check the research? I'm pretty sure it's right, but homelessness isn't over so we can't spend any amount of effort on something else because that would be inefficient.