[NoDOHC]

A few thoughts from yesteryear:

Believe it or not, 20 years ago, a lot of people were going the staged route. This was before turbos could make more than about 2:1 pressure ratio. The trick to success on a staged setup was (and still is) dual intercoolers.

The boost from the first turbo is cooled before it passes through the second turbo, and then it is recooled after the second turbo. This allows for reasonable charge air temperatures, while minimizing lag.

On a diesel (as has been noted) the intake air temperature is not an issue for engine longevity (except for possibly the valves). It is an issue for charge density and thermodynamic efficiency. This (and new NOX emissions standards) is why almost all modern diesel engines have intercoolers.

I have seen many diesel engines with staged turbos and a gaseous-fueled engines with staged turbos (good detonation resistance).

Benefits of staged turbos:
Quicker spool of smaller turbo
Insane power potential from larger turbo
Cooler charge air with very little if any more boost lag due to intercooler volume.
Very high boost potential (120 psi + boost).

Drawbacks of staged turbos:
Underhood piping disaster
Increased EGT from engine
Increased EMAP from engine
Higher cost
More potential failure points.
Insane underhood heat problems

Here is the reason that the turbos should be connected in the standard staging configuration:
Turbo Flow Maps are measured in inlet volume (or mass) per time. (Typically CFM, lbs/min, etc.) This means that at 2:1 pressure ratio on the primary turbo, with a well cooled charge, the secondary turbo will flow twice as much as it is rated on the curve, as the air is twice as dense going into it. This means that the secondary turbo needs to be 1/2 the flow rate of the large turbo (for this example).

Actually, the density ratio is what actually determines the turbocharger flow rate ratio. a 1.5:1 density ratio across the primary turbo means that the secondary turbo should be 2/3 the size of the primary turbo.

On the exhaust side, the air is very hot coming out of the engine. It is also under very high pressure. The exhaust turbine on the turbo charger is rated in pressure ratio. This pressure ratio across the turbine varies with air flow rate.

High pressure air from the engine does not occupy as much volume as lower pressure air coming out of the secondary turbo, thus the flow rate through the large turbine is a factor of the exhaust gas density ratio across the secondary turbine (the temperature will decrease some). Thus the output flow rate of the secondary turbine is significantly larger than the input flow rate (in volumetric units, obviously the mass flow rate is constant, due to the conservation of Mass limitations in our non-nuclear internal combustion engine). The larger turbine requires a higher flow rate, and must therefore come after the secondary turbine on the exhaust stream.

If the large turbo was first, it would spool very slowly, while the small turbine would quickly overspeed.