Why is it impossible to solve, say, Puzzle 71, this way?

Start: 400000000000000000
End: 7fffffffffffffffff
Total keys = (7fffffffffffffffff - 400000000000000000) + 1
= 4 × 16¹⁷
= 2² × (2⁴)¹⁷
= 2⁷⁰ ≈ 1.18 × 10²¹ keys
Start: 5HpHagT65TZzG1PH3CSu63k8DbpvD8s5iuPxgLR7vrH93n5zQhe
End: 5HpHagT65TZzG1PH3CSu63k8DbpvD8s5izj98VnVcphdvhm3msh
So you need (18 characters) endings from "uPxgLR7vrH93n5zQhe" to "zj98VnVcphdvhm3msh".
Last 18 characters (Base58):
Base58 characters represent log₂(58) ≈ 5.857 bits each
18 chars → 18 × 5.857 ≈ 105.43 bits
Possible combinations: 2¹⁰⁵.⁴³
Total keys to check: 2⁷⁰ ≈ 1.18 × 10²¹
Assuming 1 billion (10⁹) keys/second:
Time = 1.18 × 10²¹ / 10⁹ = 1.18 × 10¹² seconds....
Imagine you're trying to find a single specific grain of sand on all the beaches on Earth. There are about 2^62 to 2^63
grains of sand on all beaches combined. Puzzle 71 is like trying to find not just one grain, but a Puzzle 71 (2^70) = 157.4x Earth's sand. Even if you could check a billion grains every second, it would take you thousands of years to go through them all.
