> The PoW is suffice if the hash begins with a certain number of 0s
This is a common explanation of PoW, but is actually incorrect. If you think about it, this would mean that the PoW difficulty could only increase (or decrease) by a factor of two. In reality, the block hash is simply interpreted as a (very large) number, and this number must be less than some other very large number (the "target"). So you do end up with a lot of leading zeros -- but these are just a side effect, not the thing being measured.
This is a common explanation of PoW, but is actually incorrect. If you think about it, this would mean that the PoW difficulty could only increase (or decrease) by a factor of two. In reality, the block hash is simply interpreted as a (very large) number, and this number must be less than some other very large number (the "target"). So you do end up with a lot of leading zeros -- but these are just a side effect, not the thing being measured.