Seating areas can't be as tight as they once were, but new build terraces allow for the maximum density of spectators permitted by the Green Guide and therefore local authorities. Older terraces tend more to being compromised in terms of modern safety regs, and are therefore licensed for lower densities (such as the SS in recent times)
The maximum density for the number of spectators in a standing area is 45ish per 10msq (without checking) and that number is reduced when certain other factors are deemed insufficiently "safe", such as the strength and arrangement of crush barriers. The replacement SS will obviously achieve 45ish per 10sqm, the classic SS presumably did when it had a certificate for circa 10k, it certainly wouldn't have been higher than 45ish
You're right of course that the increased rake will make it taller relative to its depth