Add the exact phrase if it fits naturally and is genuinely relevant, but don’t force it, because a page already ranking for variants is usually a minor optimization away from done. The split is simple: natural and low-risk, yes; contorted or assumed-necessary, no. If you can work the precise phrase into a heading, a sentence, or an answer where it reads cleanly and matches what the section actually covers, it’s a low-cost move that might capture the exact-match query directly. There is little downside to making the page say, in plain words, the thing people are typing.
The reason it’s only a minor optimization is that ranking for variants already tells you Google understands the page. Semantic matching means it doesn’t need the literal phrase to know your page answers the topic. So adding the exact term isn’t unlocking a capability that was missing; it’s nudging at the margin, tightening the match on one specific query rather than teaching Google something new. Treat it as a small refinement, not a fix for a page that is otherwise underperforming.
Where this goes wrong is at either extreme. Stuffing the exact phrase in repeatedly to try to capture the query degrades readability and signals nothing useful, since repetition isn’t what wins the exact-term contest. The opposite mistake is refusing to touch a page that ranks at all, as if any edit risks the variants you have. A single natural insertion of a relevant phrase does not jeopardize existing rankings, and skipping an easy, genuine improvement out of caution leaves a small gain on the table for no reason.
The deciding question is whether the exact phrase actually belongs. If your page genuinely answers that precise query, find the one or two spots where the phrase reads as if it were always meant to be there and add it. If it would require bending a sentence or padding a section to fit, leave it out and trust the variants you already rank for. Add it only where it fits naturally, and don’t manufacture a home for it.