That couldn't possibly be the case as when the FAA was originally passed Congress' Commerce Clause powers were relatively narrow and it would have been inconceivable that the FAA could apply as broadly as SCOTUS now applies it.
In order to get to where the FAA is now, SCOTUS had to jump through multiple dubious interpretive hoops, including some dubious textual hoops as the FAA on its face clearly speaks to the types of commerce (e.g. railroads, shipping, etc) that were within its regulatory ambit at the time of passage. By any reasonable interpretation the more general terms SCOTUS leverages would only apply to those areas traditionally understood as interstate commerce, but SCOTUS wasn't trying to be reasonable--they had a goal to minimize Federal case load, particularly related to class actions (which the conservatives detested for other reasons, as well), and set out to achieve it by hook or crook.
Certifying a class is a lot easier than thousands of individuals going through repetitive arbitrations. And of course, there is the benefit (for the corporation) that a large percentage of people will find arbitration too burdensome.
Not true at all.
Are there actual examples of cases wrongly decided by arbitration as a result of this phenomenon? Maybe they are all hidden under NDA.