OK, let's phrase the question positively:
Why would anyone want a 375Ruger when the 375H&H already exists?
For the same reason that the 300 Win Mag was developed.
The 300 H&H already existed. The 300H&H was, and is, a great caliber. But the 300 Win Mag fit everything into a standard 30-06-length action, plus having a capacity with 3 grains more. (NB: the same argument does not work equally for the 300WSM, that cartridge is shorter and has less capacity than either the WinMag or 300H&H.)
Smaller, non-magnum-length actions/rifles are often
less expensive,
more common, available, and
lighter.
The result can be an easier carrying rifle.
As an example, my wife readily chose an 8lb Ruger Alaskan with a 20" barrel in 375Ruger for under $600 instead of a 9.6 pound CZ Safari Magnum with a 25" barrel in 375H&H for $900. (Prices higher today, of course.)
As a "plus", the extra five grains of capacity in the 375 Ruger allows the option of using a shorter barrel than a traditional H&H while maintaining the same velocity.
Please note, having the choice of a 375 Ruger available does not detract from the 375H&H.
The 375 H&H remains a great caliber, as does the 300 H&H. However, some people may enjoy getting a lighter, less-expensive rifle in 375 Ruger or a 300 WinMag. Those are a couple good reasons why calibers are developed.
Let me add a forecast. If the 300 WinMag is any kind of precedent, the 375 Ruger will have a good future. However, because 375 is not a common caliber for general North American hunting, I do not think that the Ruger will achieve as widespread acceptance as the 300WM. Nevertheless, in areas where the 375 H&H is a common caliber, the 375 Ruger is going to continue to grow in popularity. Mossberg, Howa, and Ruger already produce factory rifles in 375 Ruger and I've seen custom rifle makers listing 375Ruger in their caliber choices. Hornady, Doubletap, and Swift offer ammunition and Nosler has listed its brass in 375 Ruger, besides the excellent stuff that Hornady has been producing.
Here is a picture of the two rounds under discussion:
I can personalize this by adding a picture of the 375Ruger alongside a 500 **NOT**PERMITTED**:
The cartridge on the left is a 500 AccRel. It is a wildcat built on a shortened Rigby case. It fits in a standard Ruger Hawkeye action (!) with the bolt-face adapted, yet it can equal and better factory energy levels of the 500Jeffery and 505 Gibbs. (Why not get a 500Jeffery? That is also a great choice. I like carrying a lighter rifle and Jefferys tend to start around $3000 in price. Plus a load uses 20-40 grains less powder.)
The cartridge on the right is one of my wife's 375Ruger loads. Good looking.