It's strange but it's fully standard. I would guess it develops from the use in analysis, where o(n) is more common. You derive your formula, it has a term in it that you don't want, you observe that "complicated term's numerator = o(n)", you take your limit, and the term vanishes away. Use of the = sign makes more sense there, because conceptually you're claiming something about the value of the term. (Specifically, that in the limit, it's equal to zero.)

Just to be careful here: the difference between big/little oh/theta/omega is orthogonal to best/worst/average case.

A pedant could say that merge sort makes O(n^3) comparisons in both the best and worst case, ω(1) in both the best and worst case, etc. Colloquially, the former means "as fast as", and the latter means "slower than".

And there may be some logic behind it, because if some function is in Θ(n^3) in the worst case, then it is true that it is in O(n^3) in all cases, so maybe that is why they couple big Oh with worst case growth.

If an algorithm always runs in O(n^3), then it's guaranteed that it runs in O(n^3) in the worst case. And if an algorithm runs in O(n^3) in the worst case, then it's guaranteed to always run in O(n^3) (but not in Θ(n^3), of course). So if you only care about worst-case performance, it's reasonable to only use the big O.

Of course, what your parent comment says is also true - you could say that mergesort is O(2^n), in the worst case or in any other case, and be correct because it's an upper bound. But people using Big Oh informally don't say that because you typically want to show how good your algorithm is, so you use the tightest upper bound possible (i.e. the big theta of the worst case).