@estrogone honestly, no.
But a puppy is still going to chew, and need toilet breaks and cry. How you manage them is key, but ultimately they do need to be managed and some breeds are going to be far worse than others and not everyone is cut out for it.
Tbh, it sounds like OP's puppy is not capable of being left alone or crate trained - based on her OP and her comments about sleep - so really the play pen and crate training for sleep isn't going to work anyway.
Even if it can be...
A puppy will never have been alone a night in its life until it goes to its new home. Not all puppies can, or should, be crate trained for sleep. Crate training for worst case scenario (long term injury that requires bed rest) is one thing, but I wouldn't be impressed with someone putting a giant breed in a crate for extended periods i.e. 12 hours. Tbh I wouldn't be impressed with anyone putting any puppy in a crate for an extended period just to give themselves some rest.
Crates and play pens also aren't completely safe and I disagree that young puppies should be left in them. I know puppies that have broken their legs climbing out of their play pen to get to their human, and I know one puppy - whose knowledgable owner left it for 10 minutes - who dislocated his jaw trying to bite through his crate when it got it stuck and panicked. And chances are, if you're there with the puppy but not inside, it'll cry and cry and cry. Which won't help it.
And on lick matts & kongs...
Lick matts, Kongs and various other things are like the dog ownership equivalent of sticking a toddler in front of an i-pad. It doesn't do anything except give you peace for what 30 minutes? If that? So unless OP is going to be one of those owners whos solution to everything is 'Kong' and she has a steady supply of them...and really its nothing something a dog owner should aspire toward. It doesn't teach your dog anything useful, it doesn't teach them not to bite or mouth, and it doesn't build any relationship with you. Fine if that's what you want in a dog, and fine for OP, but it's not going to solve the underlying biting issue that OP has. The best way to manage teething is to engage constructively with your dog - not fill them up with energy in the form of frozen food in kongs or lickmatts. If you're going to do that, better to use a frozen tea-towel. They are, ultimately, a management tool. 15+ years ago, no one used them and by and large we had happier dogs that settled more easily. I have no idea why they're a 'thing' now as all they seem to do is create problems through being badly used.
And then there's adolescence which will be even harder if OP doesn't have that bond or indeed has still not found anything positive in dog ownership.
But whether or not OP does all those things, there is absolutely no way a puppy should be bringing on emotions that OP had when she had PMD.
And its really unfair on the puppy to be in a home where the only people who seem to want him are the children (which depending on their ages might be teaching him even worse habits - children are little shits for making biting/mouthing worse because of the way they react, for example - and making things so much harder for OP).