I think the risk with the .375 H&H belted mag in a double is that the cartridge is already at the top end of the pressure scale.
It's fine at standard factory pressures of 62,000psi, but there is not much margin for error.
A hand loader getting a bit careless, could easily push things too far.

The old British NE cartridges like the .470NE and 500NE for example, are loaded to 20,000psi less than .375 and .458 belted magnums.

I would not hesitate to own and shoot a quality double in .375 H&H belted mag.
When I think back about the one double that I really wish I had bought but didn't, it was chambered for that cartridge.