I am sorry, my English is not perfect. I will try to explain.
Now it is so easy to swap between image frame (this one selected by direct selection tool) and image frame container (this one selected by selection tool). Sometimes it is helpful sometimes not. Sometimes when we move the frame container we swap to direct selection without noticing and unintentionally move image inside the frame.
But we can lock only the frame container (from layer panel or by ^L). There is no option to lock only the content (image).
Sometimes during design process I have to move many frames with perfectly scaled and cropped images inside.
I would like to have the ability to lock my cropped image inside frame container and have the ability to move the frame container to different position and (do not worry about direct selection toool). I do not want to change the dimension of the frame, I would like to have only ability to move frames with locked images inside. It would be useful for such users who mostly work in modular grid.
OK, that seems pretty clear.
I find that most of the time when I move the content instead of the frame it's because I accidentally click inside the Content Grabber donut. Are you sure it's a problem withthe direct select tool? You can turn off the Content Grabber in the View menu.
No, it is not the problem of direct selection tool. The problem is that it is so easy to accidentally swap to this tool.
Most of the time it is because of the active Content Grabber, sometimes because of double-click, sometimes by clicking on the edge of the frame when the frame is selected or if two or more images are stacked behind.
I do not want to hide Content Grabber at all. It is very useful tool, but it would be nice to have the ability to lock the image inside selected frame by simple shortcut. Now I use ctrl-L on mac to hide Content Grabber, but it is global function and it is not giving me the "sense of security".
I think your suggestion is a good one, You should file it as an official feature request (this is just a forum for discussing things we'd like to see) at Adobe - Feature Request/Bug Report Form
It helps if you can make a strong business use case for why it should be added.