It sounds to me like you've found the one of the beautiful things about Kanban. The work is so visible, that you've made part of your process irrelevant. Congratulations, you've leaned out your process and removed some overhead.
Well, you almost have. You've not done away with the overhead yet, but you suspect that you can. Sounds like time to run an experiment. Talk to your team to see if they're interested in trying their next iteration without the stand up. Measure the results, and talk about both the measurements and the team members feelings about it at your retrospective.
You may find that they're already collaborating so early and often that the "getting in sync" part of the stand up is redundant. You might find that things go worse without it. In the latter case, be sure to shift the focus away from "walking the tasks" to "Alice, do you have that widget done? I'd like to start implementing X and need your widget to move forward." and "Hey Bob, you're really good at Y. I've not really done it much, could you pair with me a bit today?"
As for management not liking it, it sounds like someone needs to explain to them that there is no "One true Agile way", and that Scrum isn't the only way to run a project. Go research Kanban, XP, and all the other processes out there. Agile is all about finding what works for your team. Finding what works for you requires some level of experimentation.
Having the numbers to back up your decision to do away with the stand up should sway your management team. Remember, meetings are very expensive and should only be held if they're actually valuable.
Now, as for the title question of "What is the value of walking the tasks?", there is value to be found in doing it by starting at the stories/tasks that are almost done. By starting there, you can shift the focus from the traditional 3 scrum questions to focusing on flowing items through your system. Remember, almost done isn't Done. Kanban is all about limiting WIP and getting things to Done faster. By focusing on what needs to happen to get from Almost Done to Done, you'll get more value from your standup.