Remember the basic structure of travel nursing? The hospital pays an all inclusive bill rate and the agency must pay all compensation of any sort from that hourly bill rate. So if you want more taxable hourly, your housing stipend (for example) must go down in direct proportion.
Ashley is completely correct, the agency doesn't have to pay the maximum per diem, nor indeed any per diem at all. Here is a bit of business tax information for you: most agency expenses are deducted (sometimes called "written off") dollar for dollar against revenue. That includes just about anything you can think of, from your pay and benefits, to your housing. Except for per diems. They occupy an unusual bit of tax law and are subject to discounting by 50% before deduction. So they are 50% taxable to your agency (not to you). As a result, no agency maxes out the per diem, because the math just doesn't work out. That they pay any at all in recent years is the result of some IRS pushing to require per diems to be paid at a ratio of 60/40 housing/per diems. If agencies paid it all in housing, the IRS would not receive any tax money at all from the transaction.
There are a lot of interesting twists on this, but one I will mention here is that you can document your time away from home and deduct the difference between the agency supplied per diem (called M&IE or meals and incidentals in IRS lingo), and the rate provided on the GSA site (you will actually find a more favorable method and amount in IRS Publication 1542). I would recommend consulting and expert such as TravelTax to do this. For most travelers, deducting per diems is not worth it. You have to itemize already to even think about it, and then you have to meet thresholds to deduct (losing completely the threshold amount). In addition, you also have to subtract 50% first. If memory serves, it is Form 2106 you have to file before transferring the final amount to your 1040, and Form 2106 has you perform the 50% calculation right on it. So you can look at the form to see how it might play out at tax time with this strategy.