Because the information necessary for that is already available from the subnet mask WITHOUT the bitwise AND, e.g., with 255.255.255.0 or 1111 1111.1111 1111.1111 1111.0000 0000, you count the amount of 1s, which in this case is 24 and corresponds to that appendix in the CIDR notation. At this point, you already know that you only need to consider those first 24 bits from the IP address, making the subsequent bitwise AND redundant.
On a technical level, the bitwise operation is all that is needed. It is one calculation of the simplest kind. A CPU can do it in 1 tick. That’s why they invented it this way.
The other way that you described is the super extra ultra lengthy complicated - and maybe redundant - thing.