Toto, I find your question very interesting. I have read a lot saying that if you are doing things around the house and can't give your puppy your full attention, to keep him in a ex pen, as you are doing. This keeps him from making mistakes, going potty where he shouldn't, that kind of thing. This is what I planned to do until my puppy is well house-trained. Is that not recommended by the Hav owners here? Of course, I want to do the right thing by my babe!
I think it's somewhere in the middle. There are times that you just may HAVE to confine your baby... When you need to take a shower, when you have to deal with small children, when you are opening the oven door and the puppy could hurt himself... So for most of us, it's unrealistic to think we can keep the puppy with us EVERY SECOND of the day.
OTOH, people also need to recognize that raising a puppy is a big commitment, and the time they need INTENSE input from us is really relatively short... Much shorter than with human children!
As such, you SHOULD try to spend as much time WITH your puppy, directly supervising them as possible. How often they need to be confined, (and how well they accept it!) will vary from family to family and puppy to puppy.
Kodi came very well litter box trained, so it was generally adequate for me to have him gated in the kitchen with me, or gated right by my computer. (on a solid floor) In each case, there was always a litter box within easy reach. I made sure I got my puppy at the beginning of the summer, when I was not working, so I could give him my undivided attention for his first couple of months with us. (I know this isn't possible for everyone, but its something to think about for people planning for a puppy)
But he still did have to go in the ex-pen when I took a shower or was working with the oven. In those cases, I gave him a Kong or other food stuffed chew toy, and left him there. He sometimes fussed a bit, but that's life. He got used to it.
It is ABSOLUTELY NECESSARY to EITHER keep the puppy closely confined OR watch them VERY CAREFULLY (as in eye on them, NEVER out of sight) if you want potty training to go well. It's usually easier to supervise them carefully if you can keep them somewhat confined... It's easy for little puppies to disappear under furniture and have accidents that you may not even know about until later.
Some people use the method of "tethering", which is attaching the puppy to you on a leash to keep track of them. This didn't work for us for two reasons. First, it would have kept Kodi from reaching his litter box, which he already knew how to use, and second, he's always been VERY handy with his teeth, and he tended to chew through leashes in no time.
So exactly what method works best is going to depend partly on your dog, partly on the physical layout of the living space, and partly on your personal preference. The key, again, is the combination of close supervision and/or confinement.