One of Clancy's books (pretty sure it's 'Executive Orders') has an FBI agent that regularly goes to the range and shoots his 'for keeps' target first with no warm up at all.
I think there is quite a bit of value at looking critically at your first target and the first five or ten rounds. I try to ask myself what those first rounds tell me about my technique. Looking at them critically can tell me what needs work, how consistent I am, what might have degenerated since my last shooting session. (I envy you that get to go once or more each week; my schedule only allows me to go shooting once a month or so.) On days that I improve during a session, it is often because of what I learned about myself by thinking about those first few shots. And as implied by Mr. Clancy, it is probably a better indicator of how you will do in a real situation than those targets in the middle of a session that cause us to take pictures to post online.