The phones send text messages over GSM-R, so are extremely reliable.
I'm not sure what the fallback procedures are, but failures are fairly rare. On newer trains running with guards the procedure would probably be to go back to driver door operation, with the guard performing only passenger facing duties.
The whole DOO/guard discussion appears to be far less of a hot topic in Switzerland. On the Zürich S-Bahn network 300m long DOO trains are not uncommon, whereas longer distance passenger trains (IR and up) will generally be staffed by a conductor/guard anyway, independent of whether they perform any safety critical duties or not.
Then there interesting situations, where depending on which company is driving and conducting a train, different procedures can be used. For example the new SOB Traverso trains have doors always controlled by SOB drivers since SOB conductors are not safety critical. Whereas if SBB drivers and conductors are involved, then other dispatch procedures can be used if required. If SBB drivers are working with SOB conductors or vice versa, then there are also other procedures.
In general the focus is on technology and procedures to make dispatch safe, rather than endless arguments about which member of staff presses which button. Newer trains are almost universally equipped with level boarding and gap fillers, as well as doors equipped with lots of sensors to detect obstacles or people caught in or between them. Bodyside cameras are rare. The doors also close automatically after a certain period if nobody is detected passing through them, meaning at dispatch most doors are closed already. The rest comes down to the general Swiss concept of "Eigenverantwortung" (personal responsibility) - as a passenger you are also responsible for your own safety and the consequences of your actions.
On the older EW IV trains there were several incidents of guards getting caught in the doors during dispatch, having given the right away. This led to the procedures being changed and SMS dispatch becoming mandatory, meaning RA can only be given once the local door is closed, increasing dwell times slightly.