That is actually the terminology prescribed by the BBC (and I presume others) in its style guide.
This is not neutral terminology, though. It accepts one ideologically driven term and rejects the other for no apparent reason. If we want to label one side as in favor of abortion and the other against, then we should do so. Nobody really rejects the term pro gun, pro gay marriage, etc., as shorthand for what they want to be legal except for the pro abortion advocates.
I can very much see where you’re coming from, but I think the authors of the style guide would argue that pro-life represents an editorialisation of that side’s position (as whether foetuses are “life” in the same sense as people who have been born is a controversial subject) and anti-abortion is a perfectly fair description which the pro-lifers would have not deny applies to them, whereas “pro-choice” is the only accurate descriptor of the other sides, as they are not actually “pro-abortion” as in seeking the most abortions possible, but their guiding principle is a woman’s right to choose.