Is it a good idea to deposit directly into a service when withdrawing from another?

I've done that, successfully, but only with negligible quantities of low value alternative crypto assets.

I would never do that for high quantities or valuable assets such as Bitcoin, in order to help easier issue tackling in case everything that could go wrong goes wrong.

Imagine something went wrong at the destination exchange and your deposit isn't recognized.

If the destination exchange wants (for some reason) send the funds back to the exact same invoice address (weird, because reusing invoice addresses is universally discouraged, but...), it would be better that invoice address to be yours than of the source exchange. Maybe the source exchange isn't well wired into recognizing source funds in that invoice address automatically.

If the destination exchange wants some kind of source ownership proof from you, a simple problem will go through a solution unnecessarily contrived compared to if the ownership is yours.

Fees maintain the network alive. Save in headaches, save the network, pay fees.

Many services explicitly warn users against this practice, including in their withdrawal terms clauses like "you may only withdraw to an address which is controlled by you." This is likely to be due to the details of procedures used in the case of dispute resolution, but I've never seen any explicit justification for it.

The advantages of withdrawing directly are (1) saving the network fee associated with the transaction from your intermediate wallet to the receiving service; (2) overall the transaction would be faster.

The disadvantage is potentially violating the terms of services and the associated risk.

I admit to having taken this shortcut occasionally, but I would tend to avoid it for large transactions.

If you want to deposit or withdrawal bitcoin then you will definitely need a btc wallet. Usually when you create a broker account you get a wallet and address with it. Now if you want to transfer btc from one broker account to another then you will just need the address of the second account and you will be good to go.