The real problem is illustrated in the title of this thread. I have no idea why so many people refer to catcher's obstruction as catcher's inference, but they do! If called, and properly thought of, as catcher's obstruction, then it would be treated like any other obstruction - a delayed dead ball. But if thought of incorrectly as catcher's interference, then you may just kill it by calling "dead ball" if you're an umpire, or arguing for a dead ball if you're a parent or spectator.
For two reasons: In baseball, it's catcher's interference, and since that came first, it's what people know.
And, since words matter, by definition, it's an act of interference and not obstruction. I'm not talking the made-up softball definitions. I'm talking the actual English-language definitions. The act itself does not "obstruct" the batter, so I could see how people who know what the two words actually mean could get confused.
As someone who grew up playing baseball, and has too much free time to think I always thought of it as
1. I interfere with someone's ability to make a play on/with the ball. In this case the batter trying to hit the ball
2. I obstruct someone's ability to move.
This is a correct interpretation of what the words mean, but the people who wrote the softball rules had to get it wrong by trying to simplify.