Silly names for things or using baby words didn't slow down how fast I learned to speak, or how properly. Despite my generally crappy typing, I speak very properly and clearly in public, even large lectures and radio broadcasts. There's a time and place for both baby talk and proper speech. Babies should hear both, I believe. Language is fun! And there's often something very poetic and rythmic and loving about some of the ways we change words, so I think there's a purpose to that too. I've certainly heard Japanese and British people use baby talk, and people don't complain about their "lazy speech" generally. If it's only on a weekly basis, I think it'll have very little lasting influence.
The kids I know with rotten speech seem to have parents and peers that rarely speak properly at all, not because of an overuse of "baby talk". The speech pattern at home, and then the pressure at an older age to sound like their peers look like the biggest influence. Though I'm horrified at the speech of many teachers. I wish more of them would take a public speaking class! It's an interesting process, learning to tailor your speech according to the situation. Using overly formal speech in informal setting, or with people who don't speak that way can be socially distancing - they might feel you're cold, or elitist. Overly casual speech in the wrong setting makes some people feel you're improperly intimate, or frivolous, or less educated. Interesting area to think about. It's more complex than that...slang, vocabulary, grammar, speed, accent all shade speech differently. I have worked with some teenagers to learn how to be more formal in the workplace and on the telephone, for instance, since they build up certain habits by only using the phone generally with other teens.
On the grandparent issue, I had so many as a kid we had a broad range of names for them in order to keep my 10 grandparents and greatgrandparents straight. (grandmom Lastname and grandpop Lastname, mom-mom, pop-pop, nana, poppy.) So whatever works for the child and the grandparent seems to be the winner.
around my house we often use the baby word, the correct word, and the spanish word...usually 2 out of 3 in any given coversation. "I wuv oo." "I wuv oo, too, honey, I really love you." Reflecting back what she said as a way to encourage and reinforce her words, but also modeling a better pronunciation/translation for other people present.