This is in reference to the ancient Roman time period.
Romans used V instead of U because curved lines are harder to carve into stone.
I've heard this in my childhood (and heard others repeat it), but I can't find any evidence that this is actually the case.
I'm aware that U wasn't a letter back then, and V was used to make either a "u" sound or a "w" sound. My question more has to do with the shape of the letter.
Could the Roman V be written either with straight lines (V) or with curved lines (U)? If the answer is yes, then there might be some merit to the claim (you might write a U some places, but carvers would always use V because it was easier).
But if V is correct and the U shape wasn't in use back then, then the claim of "easier to carve" seems to fly out the window.
The premise of the last bit you've written doesn't make a great deal of sense to me. There doesn't have to be an alternative way of carving the u for the shape to have been picked for simple carving. For what it's worth, most of the capital letter forms -- the sort that we see inscribed in stone -- in Latin seem to have been carving-friendly, but since these are the form intended for stone-carving, that's not particularly mysterious. There are a lot of straight lines. A few curves do show up, particularly with the broad circles in O, C/G, P/R, and S.
Worth noting, though, is that these aren't the only forms of the letters that existed. Just like we have different fonts that lend themselves well to different uses, there were significantly different letter forms used in handwriting instead of inscription. Pages 13 and following here show what Latin cursive looked like, and you can see in particular a variety of "u" forms used here. The Dacian tablet on page 14 shows a u that is sort of in-between a u and a v; the first line has several ("iulium iuli" reads the first pair of words in the text) that are easy to spot. The Vindolanda tablet below, however, has a very curved swoopy sort of "u" -- harder to find, but if you look at the bottom line to the right of the large mark running up the tablet, you see the word "iucundiorem" where the first u is lost but the second is quite clearly visible. Distinctly curved "u" can be seen in the other Roman cursives shown. It's worth pointing out that by the time you get to the 4th century example on page 18, you are starting to see a separation in how the consonantal u (which gives us our v) is drawn versus the vowel u. This is easy to see in the last reproduced line, which ends "-orum provinciae." The u is shallow and lifted above the line, while the v is more of a broad swooping u-shape that occupies the same minuscule line as the rest of the letters.
Thus, there were various ways of writing all the letters. The clean, straight-lined and broad, steady-curved forms of the classic capitals used for inscriptions are well-suited to that way of writing, while various ways of writing quickly on wax tablets or in ink had their own letter forms.