[roadster]

Have you actually had any warnings when running pressures which are not close to target settings ( high or low ones)? One of my tyres was several psi low on delivery but it didn't trigger any alert. I suspect the permissible range is a bit wider than it would be for an ordinary car given that off-roaders might want to drop tyre pressures to suit conditions. Perhaps warnings are only triggered if the is a sudden drop in pressure on one corner only.

 

[roadster]

I suspect that higher recommended pressures on low profile tyres are aimed at preventing rim or sidewall damage if you hit a rock or a kerb. It is standard practice to offer larger wheels only with lower profile tyres in order to keep the rolling radius about the same and therefore match gearing and related emissions figures without mechanical changes or re-homologation.
For some strange reason bigger wheels with low profile tyres are seen as an "up-market" feature that manufacturers insist on putting on top-spec models. Having had a sidewall destroyed by hitting a protruding concrete lump at 70 mph on a low profile set-up (45%) I know how vulnerable they can be and I was very lucky that the wheel was not damaged too.
Because the tyre is also wider the static deflection under extra load shouldn't be any greater but even if the extra deflection is the same there is far less margin when hitting something solid.