Good idea but not easy to enforce

You need to put youself in the baby's shoes or relative/friends' shoes before making this controlling decision.

Baby will feel the love by enjoying presents from other people than parents such as TOYS!  This is also an opportunity for you to tell the baby that (1) so many people are care about/love her - easier for her to remember who's in the family although they are not live in the same city; and (2) start the idea of give and sharing.

Your relative/friends probably not like the idea as you are taking away their idea of love or personal present to your daughter.  A lot western people think money is not personal enough.  What happen if they do buy toys?  Will you ask them to return and give the money to you?  You don't really want deal with this type fiasco!

If you are affair that they will buy inappropriate boys - just let them know that they check with you before place the order or you create a list of appropriate toys during special occasions.

Just my cents being a Mum.