Absolutely. This has been true throughout my entire career literally everywhere I worked, on-site and remote alike.
What makes my experience a little more representative (or so my ego says) is the fact that I am from Eastern Europe. Ever since several years now (3-4) we are no longer that attractive IT outsourcing location because a lot of people around here learned their price and value and charge normal (if still below USA's) rates. And thus many businesses started trying to outsource cheaper to Africa and parts of Asia.
The results have been catastrophic and hilarious at the same time. I've been called to "fix the mess" 6-12 months later by five businesses now, and I outright told one of the business owners that he'll have to pay me $20k a month to fix something as non-salvageable as the dumpster fire I was given. He refused which was a win for me because I still value my time and sanity.
So many businesses look at this outsourcing to cheaper staff thing very superficially, as you said. Sure you save money the first 2-3 months. Absolutely, you do. But then all the unfinished and badly done work starts peeking from the edge of the window.
And finally, you are also very correct when saying that hiring the managers that govern these people efficiently effectively destroys the cost savings.
In conclusion: I have definitely observed the same as you.
(Several edits: apparently I had a stroke and wrote some really broken English here and there.)