What IRS has done in the past with Forms 4852 is not a prediction of what they will do in the future.  They could have done a special project on it three years ago, sending out notices to all alleged employers, or they could have done nothing for the last ten years and make 2022 the year they catch up on them.  My guess, though, is a paper-filed 4852 has less likelihood of follow-up, because you haven't already sent the data in a form they don't have to transcribe.

Where do you draw the line, though, between "nanny" and "babysitter."  A nanny is live-in household help.  Someone who goes home every night, and maybe babysits other kids at times, might be a Schedule C filer.  And qualify for QBI deduction.  Especially, if at the start of the year there was no certainty about how long the gig would last.