To want one? No, dogs are lovely. To get one? Maybe. It would certainly be hard, and almost certainly harder than you expecting. You will never have another lie in for a start!
The day care thing isn’t insurmountable. It’s a pain, sure. You’d have to add the time to your work day to drop off and pick up, and there would be no flexibility. However, what if your puppy hated daycare? Many puppies love it, but my dogs would hate it. They want a day of quiet snoozing, a sniffy walk and five minutes zoomies. But they never, ever want to be away from me. Not my daughter, not the dog walker, not Mx Daycare. Me. Dogs are individuals, and there’s no guarantee it would be ok with your plan for it.
The flat would bother me more. Toilet training puppy in a flat? You have to take them out every thirty minutes and presumably they can’t go to daycare until they have all their jabs. They need containing when they are small became they destroy everything and you and your partner both need to be onboard. Puppies are seriously intense and adolescent dogs are challenging.
If you could rehome a dog, which is known to be sociable and enjoy a daycare type setting, and can be trusted at home (and is housetrained) maybe, but few shelters would give you a dog on that basis (I think) and there’s reason for that. I recently got two because it helps my daughters anxiety. It has, but man I’m fed up of the responsibility. I’d just got past the ‘needing to be responsible for another beings bodily functions/being nagged into playing/feeding/letting in/letting out/getting up at night/never being able to go out unless I find a sitter (they have separation anxiety, and one is ill. I don’t expect it to last, but it takes time to solve these issues). It’s like having a toddler again. There are huge upsides, but the downsides are equally massive. And my dogs are older, housetrained, generally sleep though (Illness notwithstanding) pretty chilled, and can just be let out in my dressing gown. I’ve had dogs before and knew what I was getting myself into. And it still sucks a bit for me. I can’t imagine having to get dressed and take them for a walk every single time they needed to go out, even with adult dogs (I routinely let mine out first and last thing, plus mid morning, mid afternoon and after dinner, in addition to their walks). Over Christmas, the sick one needed to go out every two hours, day and night. And then I needed to hose down. Your dog will get sick (they all do, sometime. They eat ghastly things and aren’t even sorry!). She’s still sick, and isn’t sleeping through, although it is better.
Can you foster or dog sit and see what its really like? If you haven’t had one, you might be a bit naive (fair enough. Everyone starts somewhere with everything). Your partner might have a point. It’s not undoable, but it would take a lot of doing, I think.