IME this perception exists because (as I have repeatedly seen at clients) the absolute most junior people are hired as testers in order to keep costs down. Because they’re so junior they don’t contribute very much. 1/2
The “5x to 15x” cost of automation proposed by the OP fits with this model: median developer pay is around $150k US. A team of five devs then costs ~$750k annually (considering TC only here)
The cheapest QA analyst costs 17% of a dev salary.
Add to this that test automation is a senior dev activity. It isn’t taught in school nor in boot camps. Nor can you learn it at just any dev job.
Now let's look again at why cheap junior QA teams are so popular.