To answer your question concisely, no, the word “might” isn’t a significant enough criterion in Romans 9:23 to judge an English version’s “accuracy” based on its presence or absence. I think the key is to avoid embracing a strict sense of only possibility if “might” is present.
A good example is the famous verse John 3:16. The second half could be translated, “that whoever believes in him might not perish (subjunctive, ἀπόληται)…” Is it only a possibility that someone who believes in him will not perish? And perhaps just as possible that they will? Of course not. The subjunctive is used for the grammatical reason that it is in a purpose clause (“that” is ἵνα, hina). As long as we don’t read a strictly possible sense, “might not perish” is still a good translation.
To expand more on the answer, the use of the English “might” or “may” is a classic, and now, I would say, an outdated way of indicating the subjunctive mood. For example, of the 59 English versions on biblegateway.com, only 14 include “might” when translating γνωρίσῃ (gnōrisē) in Romans 9:23. Bill Mounce, in a blog precisely addressing this topic (https://www.billmounce.com/monday-with-mounce/my-second-thoughts-about-subjunctives-purpose-clauses), fears that often the word “might” introduces an unnecessary and sometimes harmful conditional element. “Much better”, he says, “to generally define the subjunctive as indicating something that is not ‘is’ but is ‘uncertain but probable’.” In other words, “the subjunctive is one step removed from reality,” but not as far removed as the optative, which is only “possible.” Blass and Debrunner, in their Greek Grammar of the New Testament, point out that a purpose clause using ἵνα, as we find here in Romans 9:23, “often serves as periphrasis for the infinitive.” Therefore, versions that translate γνωρίσῃ here as “in order to make known,” like the ESV does, are well within sound Greek grammatical and syntactical use.