Yes
> can start working immediately
Abso-lutely not. Check out Reddit to look for accounts of how the transfer works and see how easy it really is...
When you transfer, you need a lot of cooperation from the new firm as they have to be ok filing paperwork, they have to do it in a timely fashion, and due to processing delays on the order of weeks (if all goes well) you cannot start work immediately. For many, many employers, this puts you at a strong disadvantage against applicants who are all good to go and ready to show up for work on Monday.