The Bitcon network is not an onchain transaction, which can't be visible on the blockchain,
I assume you are saying Bitcoin network is oncoin transaction and everything moved is visible.
so sending the bitcoins bit by bit into different wallets, even if it's up to 100 wallets just for them to be split, all the wallets can still be linked from where they were sent to where you will send them; they can all be traced on the blockchain, and anyone who knows you own the first address will definitely know you still hold those coins at a different address.
I am talking about privacy, not anonymity. Keeping things private doesn't necessarily mean the user wants complete anonymity its all about the choice and who can get to know what I do. Obviously even if the funds moved to 100 different addresses instead of 1 the link isn't broken and can be traced back to its origin and it is not going to help if someone wants to hide their traces.
But this will be helpful if you don't want someone you know how much you have left in wallet B.