The problem area is not the first stages of the compressor. You are far from the limits there of the usual metals used (no-one is using aluminum in engine compressors). The normal material used is titanium for the first stages and then Ni alloys, where the creep limit is at 700°C. This is the real limit, this is why you use low compression engines for fast SSTs.
Yes the basic problem is creep at elevated temperature.
The Olympus engine started it life, aimed at the subsonic Vulcan, with Al alloy LP blades. When it evolved to the Supersonic (limited duration) TSR2 it adopted steel blades for the LP first stage with LP Titanium blades in the stages behind it, and the first few HP stages, where you are correct the latter stages of which used nickel alloys. There are other reasons for a steel LP first stage if you have Ti behind;- best chop up anything incoming rather than risk it detaching the Ti blades behind and setting the whole lot alight.
When further developed again for Concorde super cruise capability, the engine was “zero staged“ whereby a steel bladed LP fan added at the front. Following a series of Titanium fires within the compressor, the titanium blade stages were progressive swapped to steel, I understand at least for the whole LP, maybe the forward HP stages as well.
The Titanium fires were a result of the extended operating times at high temperature, the blades creep excessively, the tips rub on the casing, and the local friction generates sufficient heat to ignite the Titanium. Not a problem for most supersonic dash applications.Of course the stators remained Ti.
When a titanium compressor fire occurred the results were spectacular;- the engine was quite literally cut in two. To remove it, tubes were welded across the gap to restore the basic integrity such that the could be lifted out.
I was told this problem has been also observed on the very few other engines specifically intended for Super cruise flight, e.g the J58, the but I’ll honest and say I’ve never seen detail of the blade material.