Beginning again, considerably easier when bankrolled by a significant amount of wealth lol
While I do understand the sentiment that the value of the gold paired with its extreme, near insurmountable weight, is meant to represent a the hurdle which cannot be overcome and the Courier's own personal obsession with which to battle, I would argue that it is equally representative of the themes to have the Courier clean out the casino vault.
Every step of the way, the Courier's role in the story is not a representation of blind obsession like that which can be so easily seen in the other characters, but rather the Courier is the catalyst through which we see change, the disruption of the status quo that was hunger, greed, malice, etc. The best outcomes have the companions influenced in such a way as "let go" of their own obsessions, and being incapable of doing so, is what ultimately leads to the final demise of Elijah.
For the Courier, however, there is no build up to "be ready to escape with the gold" presented in the DLC, the treasure had previously only been described by Elijah as valuable for his own plans. In other words, the gold was never presented so clearly as an obsession for the Courier, not so much as basic survival or revenge against your captor were presented as motivations. While learning when to let go was absolutely the theme of Dead Money's setting and characters, in terms of the Courier's own story it is much more applicable to the much later DLC Lonesome Road, where the Courier (and Ulysses, for that matter) must confront their histories, with loss and letting go being a theme. The clone ED-E, the choice to launch the nukes, what becomes of the fate shared by two couriers: this is the instance of slow building tension across the multiple DLC arc where the tones letting go would actually resonate.
The Courier, in successfully removing the gold from the vault, is only continuing to be a catalyst. The Madre is described and referenced as a character in its own right, especially by Elijah, so cleaning out its vault is thematically consistent; the Madre a trap built of hate an malice, "letting go" of its dark intent. In sealing the vault and leaving it empty, the Courier is finishing the work that its creator, in a last minute change of heart, attempted to do himself, but was unable, thwarted by the war.
Escaping with the gold is a kindness.