There's no downside to claiming a dependent in some years and not others.
I will take your word that there are no tax benefits for claiming a dependent, I haven't evaluated your particular circumstances. Any tax benefits you could claim would require that you have the child's SSN and file by the deadline of an "on time" return, which this year is October 15 as long as you apply for an extension before July 15.
You can't claim a dependent without an ITIN or SSN. I don't know what your preparer did in 2018, but the IRS would not have given you credit for a dependent without a tax number.
