Thermal shutdown in a low power app might be unnecessary.
It seems unlikely that 1W dissipation is a safety issue. But
such requirements often flow down from conservative
system requirements and no particular local reality.
With 125C operating temp and a probably foundry process
application rating of 125 to 150C, there is not much room for
the overtemp circuit's tolerances. So personally I resist
having such features in my extended temp range parts
unless the customer really wants it