Especially when sight-reading, it's helpful to look ahead and plan your fingering. In this case, with such a short piece, it's easy to see that the B is the lowest note and G is the highest. (So we can't pick any one hand position that gives one note to each finger. We'll have to either do some stretching, or move our hand at some point.) We can also notice that there are two of those Bs in the first line and one near the end, and only one G in the piece, at the start of the second line, so maybe we'll need to move just before that G. We even have time to imagine trying out certain options before we start.
(With the disclaimer that my primary instrument is violin): I would start with 2 (index finger) on C, to be prepared for those Bs. I would prefer not to move my 1st finger (thumb) from C to B, simply because any time you play two notes in a row with the same finger, it creates a small gap between the notes as you move.
At the end of the first line, once we've gotten the Bs out of the way, I would prepare for the G by switching from 2 to 1 (from index to thumb) for the pair of C half notes. Finally, now that I have 1 on C, I'd be inclined to handle the final B by crossing my 2nd finger over my 1st as you describe (so that the last two measures are "3 2 1 2 1"). There are other valid options, including using a 4 for the E at the start of the next-to-last measure.
So why didn't I just cross over for the first "B" in the piece? Well, if we started with 1 on C, then the fingering of the second measure would be 1, cross over 2... then... 2 again for the D? That's even more awkward than moving 1 - 1 for adjacent notes. Sometimes, when sight-reading, we find ourselves having to live with awkward fingerings because we didn't notice what's coming, but it's helpful to look at least a few notes ahead and prepare. As you gain skill and familiarity it will become more and more unconscious.
By the way, let's address some of the non-answers you've gotten before when asking about "the best fingerings": Are all fingerings equal? No, of course not. You make a great example: yes, you could play the whole thing with one finger, but that would be an objectively bad fingering. Are some fingerings equal? Sure. Especially at more advanced levels, there are often multiple ways to solve technical challenges, or fingering choices that might rely on personal expressive decisions. But at more beginning, foundational levels, there are often simple, objective reasons that the most obvious fingering is the right choice. If this were a violin piece and was intended for a first-year student, I could confidently say there would be only one "right" fingering (although a more advanced student could well choose other options for expressive purposes).