I have a 7yo dd and I'll freely admit to not 'playing' with her very often, at least not as often as I probably 'should'. I sit and do arts and crafts with her, we play board games, this weekend we went out sledging which was great fun, I take her to the park and we cuddle up and watch movies, etc. But ask me to sit down and play Barbies or mummy's and daddy's? Nope.
It was the same when she was really little, tbh. I never minded reading books, singing songs, enduring soft play centers or showing her how something worked, but sitting on the floor with her all the time surrounded by loud, annoying toys bored me to tears and I didn't do it very much. I hated the baby/toddler stages - they were mind numbing. Older children are much more fun, your time with them isn't repetitive and they're not as needy and demanding. Perhaps your wife is the same. The early stages can be dull as dishwater.
I've always been a single parent and I have too much on my hands to play at being a clown 24/7. I work part time, I have a dog to walk, a house to clean, washing and dishes to do... Something has to give and it can't always be the housework. Some parents just aren't natural, gushy entertainers. Some parents relish the idea of playing with their child for countless hours and some don't. Your wife has three little people to keep up with and that is a massive amount of work for any person - it's exhausting. You've said she's the primary carer right now so I presume she's at home with them? And if she's staying at home would it be fair to say she's doing the lions share of the housework, washing, dishes, cooking, running the children to clubs and school, etc? She'll be run off her feet, OP. I only have one child and on an average working day where I've been up since 4.30 am I can guarantee you the last thing on my mind after collecting dd from school is playing Sylvanian Families.
You've said all three of your children have been whiny and miserable. It sounds like you've just had bad luck in the whiny and miserable baby department. Some babies are just naturally grumpy. There's often no rhyme or reason to it - it's like playing the lottery. My dd was a very happy, smiley little thing and still is. But I didn't spend all my time playing with her to make her that was - she just was that way. You've said that your wife is a loving, caring mother. I think you need to cut her some slack and stop comparing her to others, tbh.