I wouldn’t say you become “better,” but you adapt quickly. Superficial and unimportant activities fall away. Things you used to think were important don’t seem to matter as much anymore. Time simply becomes more precious and you do as much as you can not to waste it.
Since becoming a father 3 years ago I think I’ve become more productive. I still struggle to prioritize and my energy/drive is certainly less than what it used to be (especially after our second child was born). I began outsourcing many of the activities I was handling in my business (cold emailing, web development, etc.) so now I’m learning how to be better at delegating tasks and managing people.
The important thing to focus on is becoming adaptable. You’ll adjust to a “new normal” and then your kid’s sleep schedule will change. You’ll adjust again and then they won’t eat the same foods anymore. Kids change so much so fast that even if you get set in a routine it’s bound to change. Or at least that’s what I’ve experienced so far.
I don’t want to assume this will naturally happen to you. It might be harder or easier for you to adjust. However, you’re asking good questions going into parenthood so I think you are willing to adapt and learn!