I can't think of a single case where that's been true, in either my experience or anyone else's.

The contract language comes into play when everything has already gone to hell. Yes, there needs to be a contract. But you should never assume it will give you any particular leverage over a larger, well-represented client who has elected to take an adversarial position.

The above is clearly a situation where contract verbiage for transfer of rights would make any subsequent conversation on the topic very short. However, as to your general point, what do you suggest? Is that risk something that can be mitigated, or priced into your rates?

There were already lawyers working for both parties before they signed the contract. Nobody has to find one just because there was disagreement.

One of the things I've learned from Patrick Patio11 is that negotiations should be on scope not price. The implementation is that clients who expect me to deliver something they cannot afford aren't worth taking on.