I think your title is unfortunate, and your initial concern about whether the responsibility for entertainment lies at your wife's door (rather than your own) jars a bit, but in your latter posts I think I can see what you're asking?
If you're saying 'does a PARENT make a baby happy if they play with them' then it's a reasonable question.
I often feel inadequate as a parent, because I seem to have given birth to needy little toddlers. Everyone else had sunny, demur, quiet toddlers, not screechy, wriggly, busy little creatures like mine! However my eldest is school age now and is very gentle and thoughtful, and delights on making people laugh at his antics. He's got through his teething, his reflux, his glue ear and subsequent poor language skills. Now I feel a proud mother and not an inadequate one, because HIS stage moved on and he is now a delightful little happy boy.
I have read articles that warn parents about helicopter parenting when it comes to play. Of course do so I you wish, and there's a place for it, but apparently if you do it too much you rob them of their independence.
I sympathise with your wife and agree with her that she can't realistically be expected to perform tricks for them. But as other users suggest, maybe you could take on that task from time to time 