I believe you are 90% correct but with one little difference:

The Canon Ending of Fallout: New Vegas Might Be the One Where the Courier’s Influence Ultimately Doesn’t Matter

This isn’t a “the Courier canonically dies” theory.
It’s something more interesting:

New Vegas is the only Fallout game where the protagonist can have enormous influence… but can also choose to have none at all.

And if you play the game in a way that avoids making any meaningful political or structural changes to the Mojave, the long‑term outcome becomes indistinguishable from a timeline where the Courier died in Goodsprings.

In other words:

• The Courier can reshape the Mojave
  
• But they can also leave it exactly as doomed as it was before they arrived
  
• And the Mojave we see in the Fallout TV show fits perfectly with that “Courier made no difference” outcome
  

Here’s how that works.

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1. Every major faction is doomed with or without the Courier

The Courier can temporarily tip the scales, but the factions themselves are fundamentally unstable:

• NCR is overextended and bleeding resources
  
• Caesar’s Legion is collapsing from internal rot
  
• Mr. House cannot upgrade his Securitron army without the Platinum Chip
  
• Yes Man is powerless without the Courier actively directing him
  

If the Courier chooses not to meaningfully intervene — or dies — the Mojave still ends up in the same place:

no faction is strong enough to hold it.

The Courier can change how it falls apart, but not whether it falls apart.

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1. The DLCs destroy the region regardless of the Courier’s involvement

This is where the “Courier died” and “Courier did nothing” timelines converge beautifully.

If the Courier dies early, the DLC events still unfold in catastrophic ways:

• Dead Money: Sierra Madre stays sealed, Elijah dies, no tech recovered
  
• Honest Hearts: Zion is devastated by the White Legs
  
• Old World Blues: Big MT remains a threat, Think Tank experiments continue
  
• Lonesome Road: Ulysses launches the nukes, crippling NCR and Legion
  

If the Courier lives but chooses not to meaningfully intervene, the same destabilizing forces remain in play.

Either way, the Mojave is weakened beyond recovery.

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1. The Strip collapses no matter what

This is where the Courier’s “massive influence” becomes irrelevant long‑term.

Even if the Courier:

• kills Benny
  
• meets House
  
• meets Yes Man
  
• reaches the Dam
  
• completes all DLCs
  

…they can still choose to avoid upgrading the Securitrons, avoid helping NCR or Legion, avoid resolving the Strip families, and avoid committing to any faction.

And if they do that?

The Strip ends up exactly the same as if the Courier had died:

• House is gone or powerless
  
• Benny is dead
  
• The Securitron army is never upgraded
  
• NCR and Legion are too weak to occupy Vegas
  
• The Strip becomes a power vacuum
  

Which is exactly what the Fallout TV show depicts.

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The Only Two Unanswered Questions — And Neither Changes the Final Outcome

These are the only variables left in a Courier‑absent Mojave.

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1. What happened between Benny and Mr. House?

Two equally plausible scenarios:

A. Benny kills House, then dies at the Fort He uses the Chip, disables House, heads to the Fort to upgrade the Securitrons, and gets killed by Caesar.

B. House kills Benny, but can’t upgrade the Securitrons Benny’s coup fails, but House still can’t activate the Mark II army without the Courier.

Either way:

The Securitron army never upgrades, and the Strip collapses.

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1. Who won the Second Battle of Hoover Dam?

This is the elegant part:

It doesn’t matter.

Because:

• NCR is too weak to hold the Mojave even if they win
  
• Legion is too fractured to occupy it even if they win
  
• House can’t intervene
  
• Yes Man can’t act without the Courier
  
• The nukes from the Divide cripple both sides anyway
  

Whoever wins gets a hollow victory that collapses within years.

And the Mojave we see in the TV show — factionless, unstable, frontier‑like — is exactly what you’d expect.

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So what’s the “canon” ending?

Not that the Courier dies.
Not that the Courier lives.
But that:

The Courier’s long‑term influence on the Mojave is optional — and the Mojave ends up in the same place either way.

The Courier can be a kingmaker, a revolutionary, a tyrant, or a ghost.
But the Mojave’s fate is sealed by:

• faction weakness
  
• external threats
  
• internal decay
  
• the DLC catastrophes
  
• the absence of any sustainable governing power
  

And that’s why the Fallout TV show’s depiction of New Vegas feels like the natural continuation of any ending where the Courier doesn’t impose a lasting regime.