I think thats nice of her, altho id prefer my dh to do. Mainly because he is a soppy sod and really puts thought into gifts from the kids.
So immagine for minute that she told you, not asked, told you, that she was going to do it. And you and DH responded that as nice an idea as it was you'd prefer HIM to do that bit. Fpr the reasons you outlined above.
And she burst into tears.
The first time you might panic, think oh shit I've really upset her. Backtrack and despite your prefernces let her do what she wants.
Fast forward a few months/years/decades...and you notice a pattern, and your own growing sense of disquiet that you are being played and forced into the bad guy role.
You might not find it so nice by the time that dynamic has become etablished and you have to push it back in a more foreceful way than you are comfortable using under normal circs.
In fact you might feel well and truely manipulated.
And by that point it is not unusual start to view all acts/pronouncemnts in a more suspitious light.
Which is why I suspect the OP didn't give an overt back story and asked to see if the granny buy, baby give present was a norm. To double check that her constant "alert to potential manipulation" state hadn't inadvertantly lead to her leaping all over her MIL for something that was actually innocent.
And possibly to find some support. Cos the sort of seige mentality that superfically innoccous whimsey can create does rather leave you feeling a bit lonely, misjudged and misunderstood.