.416 RM is a fine chambering and one your professional hunter would be happy to see you arrive in camp with you. The marketplace determines price and, the good thing, if you were looking for a .416 Remington, is that they tend to be priced lower, and sell at lower prices, than other chamberings in similar/identical rifles. For example, if you had three rifles commissioned, one and 375 H&H, one in 416 Remington in the final one in 404 Jeff , for example, then they were indistinguishable from each other with the same components, it is almost a certainty that the 404 would sell for significantly more than the others, with the 375 coming in second. In extending this example, if the same was performed with a 416 Rigby and 416 Remington, you would see the Rigby almost certainly sell for a significant Delta over the Rem.
There is no real world distinction between the 416s unless you step up to the Lazzeroni Meteor, but that doesn’t mean it is more effective in doing anything other than shooting flatter at extended distances.
Hope this makes sense as I dictated it and did not review.
In short, the 416 Remington is an excellent round. It is just not as popular as other chambering and hence the market has determined the value is generally lower than other offerings in similar rifles.