Of course.

But I didn't talk about that.

Reducing the keyspace is possible, and I can prove it.

One way to do it, is the following way:

Say we have these keys:

0000000000000000000000000000000000000000000000002000000000000000 // HEX Private Key, Hidden from us.
02ae86eeea252b411c1cdc36c284482939da1745e5a7e4da175c9d22744b7fd72d // Compressed Public Key, Known By us.

We can do some math on the curve with the public key, to help us brute force it faster - because we will brute force another key, in a smaller range.
Let's multiply the public key by 57896044618658097711785492504343953926418782139537452191302581570759080747169.

We get this new Public Key:
0206f9d9b803ecf191637c73a4413dfa180fddf84a5947fbc9c606ed86c3fac3a7

And, this new public key's private key, is:
0000000000000000000000000000000000000000000000001000000000000000.

So, if we would like to brute force 02ae86eeea252b411c1cdc36c284482939da1745e5a7e4da175c9d22744b7fd72d, we could make it 2x faster, using this method, on even keys.