But with a geared bike you set-off with a lower ratio than you would fixed
Doesn't matter, you're still going to be pushing down on the pedals just as hard. The sprocket size has no effect on chain tension, only the chainring does.
People think that a long climb effort (5 minute) has a bigger peak watt effort, than a smaller humb (1 minute effort) - but it's the other way around. You can power your way through a 1 minute effort, but you need to dose that 5 minute effort and hold back the horses.
But with a geared bike you set-off with a lower ratio than you would fixed.
If 3/32" is adequate for a HC start, then why bother with 1/8"?
HC have got to be more demanding than, eg, regular road use.