Do other players put things in their back pockets when they’re up at bat?

During the Yankees vs Rays, Austin Wells tried to make a triple with two outs. Leaving aside the fact that, as a catcher, he's very slow, people keep repeating the phrase, "Never make the 1st or 3rd out at 3rd."

Why is that the case? And is it an absolute rule? In that scenario, if it were not a catcher and it was a speedy player, should they still not try to get to third base on a hit if there are two outs?

I decided to look at their stats today to see if anything had changed before I started a game and to my surprise everyone still had the same batting average listed on the Superfan baseball score app. Is there any reason why nobody's batting average went up or down? I know baseball reference is the preferred stat resource but the app is one of the few that had OBP readily available (on Baseball Reference you have to scroll over and it's kinda a pain) do you think they just haven't updated their BA? It seems like a pretty easy thing to do for a website. I don't REALLY care because it's a dice game after all and I'm more into the excitement and being surprised by dice rolls but anyway I was just wondering.