You're assuming it is for support of the exchanger.
My opinion based on the images I've seen:
The LCC is on the high side of the compressor loop, there are two large round ports (green) that mate to the metal manifold. The LCC bolts to this manifold with 4 fasteners (orange). This connection is strong enough to handle 200ish psi x the port area. Plenty strong to handle the mass of the LCC. The LCC itself is a stack of stamped and brazed plates, also very strong.
Then look at the strap. It has almost no angle relative to the assembly, it is not constrained against sliding, nor are the corners bent (formed). This would not stop the LCC from sagging nor does the setup look correct to reduce vibration. Further, the nylon is not structurally able to provide support.
So then, what does it do? The liquid side of things is provided by two rectangular ports (blue) from the plastic/nylon manifold assembly. This is bolted to the metal manifold, but it is not fastened directly to the LCC (since they are mounted to the same piece, it's almost the same). More critically, it does not have any fasteners between the two ports.
The coolant system operates under low pressure (pump induced only verus an ICE that runs at 16psi to raise the boiling point) thus the amount of sealing force needed is also low.
My thought is that the strap fastens the cross support (red) between the ports to the LCC to provide more sealing force and keep them in contact. This compensates for any distortion in the nylon piece or relative movement due to differences in coefficient of thermal expansion. The nylon is bent (deformed) to provide preload and the natural bend of the strap does also. As long as contact is maintained, the system stays sealed.
Picture from Munro, markups mine.
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