What you mentioned is happening because US has no other options. US literally only borders 2 countries, and it sure won't be moving its manufacturing jobs to Canada for obvious reasons. For the past several decades US has been outsourcing jobs to Asia, and now it's trying to snuff out Asian industries because US is literally being outcompeted. What could possibly be safer than to move those industries to a weaker, poorer nation right next to you which you have infiltrated inside out? US has a high degree of control over Mexico both through soft and hard power, from the Coca Cola Mexicans drink to the hard boots of US Army trampling on Mexican soil if it steps too far out of line. Have you seen the equipment of Mexican military? Even a single US State National Guard could crush them, and I think that's for a reason. Imagine if Mexico has the soft and hard power of Russia. Any of what you stated would still happen?
So in the end, you are partially correct that disparity in soft power contributes to the close US-Mexico relationship, but it's not in the direction which you stated. It's actually US soft power that dominates Mexico, not the other war around.
