You could argue that "please" has the same underlying meaning, but the pragmatics of how that meaning is interpreted can vary from context to context.
In the first two cases, the implication is effectively a command. The implication is not "You may optionally decide not to send faxes, and that would please us". It's a bit like an airport announcement saying "Passengers are invited to proceed to gate 4", which is not quite the same as if I "invite" you to a party-- they're not actually offering you a real choice to decline that invitation.
Many languages have this kind of pragmatic subtlty: if a Spanish sign says "Favor de no fumar", they're not actually implying "You would be doing us a favour if you decided not to smoke". If a French sign says "Merci de ne pas fumer", they're not actually saying "If you decide not to smoke, we'll be thankful".
In English, modals are another common area of this kind of subtly. If your boss says to you: "You might want to get this done by lunchtime", they're not making a supposition about your volition to do the task-- what they're effectively saying is "Do this by lunchtime"; I've heard cases of foreign employees getting caught out by this kind of device.