It depends on what you mean by "needed."
This is one of the (three-ish) incredibly frustrating standards I frequently see brought up in D&D discussions. Because, if you mean that in its usual sense, absolutely nothing is ever needed in D&D. Ever. There is no such thing as "necessity." Period. We don't need specific classes, we don't need specific rules structures, we don't need specific races, we don't need particular equipment or spells or feats or themes or anything.
But if you mean a specific, niche definition of "need," something like "does this have enough utility that it can't be ignored" or "is this sufficiently fundamental to D&D that getting rid of it is untenable," then it's unlikely that half-orcs are "needed," but there are lots of things present or added over time that aren't "needed." Orcs themselves don't seem to be any more or less "needed" than half-orcs. This means the answer to the question isn't very informative; we would need to ask something further, like "what does half-orc provide?" or the like, to really draw any meaningful conclusions.
That's the key problem with this question. It very, very easily becomes a motte-and-bailey fallacy, even without the author intending such, due to the fluid sense of the word "needed."
Now, engaging with the core premise of the thread assuming that "are half-orcs still needed" should actually be read as "are half-orcs still useful," my answer is unequivocally yes. I still see good things being done with them, and I still see them having a place in various fantastical settings. I don't have literal or figurative "skin in the game" when it comes to racial intermixing, being from a historically privileged ethnic background, so it's hard for me to have clear insight on that front. But I think it's worthwhile to have "child of two worlds" options, particularly given the people in my life who have been of biracial or polyracial backgrounds and who have personally felt a deep desire to explore that identity and what it means for them.
On the flipside, I absolutely, 100% agree that the disgusting and inappropriate backstory information for half-orcs from early editions has died the death it deserves, and will not dignify it with further discussion than this sentence. It should fade into obscurity as nothing more than an annoying quirk of history.