The problem is that unburned hydrocarbons that are not fully burnt in the catalytic converter can contaminate the coating on the matrix. I am sure the exhaust wrap helps but when I was offered the option of a richer coating that would start to operate at lower temperatures on the matrix of my new cat I decided to pay the extra. So far no regrets. When it is up to temperature I can even have the car running for a few minutes in my underground garage without choking on the fumes.
I would definitely try the exhaust wrap, when hot and dry I can even touch it without risking a scald, but eventually a higher quality cat may be worth considering.
An interesting note on life expectancy:
How long can a catalytic converter last?
The duration of a good catalytic converter will depend on how it is used.
Normally, after 60-70,000 Km, the catalytic power will be less than half, and the abatement of emissions can decrease from 98% to 50%. When that happens, it should be replaced.
Its loss of effectiveness is caused by a gradual ablation of the precious metals and its sintering, which is caused by high temperatures. The dispersion of the precious metals therefore fails, dramatically reducing their catalytic power.
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