"And unless you really need 3-phase, split phase is easier to deal with - with 3-phase you need to monitor all three phases to ensure they are working (failure of one phase is a common failure mode that requires immediate shutdown of the other two phases lest any dangerous currents develop)."
Losing a phase will not result in dangerous currents in the supply system. The most common three phase load is a motor. If you start a three phase motor and remove one of the phases the motor will continue to run on a single phase BUT it will try to draw more current to compensate for the loss of the phase. You now have overloaded windings and the motor will quickly burn itself out. You use phase protection relays on your motors to open the contactor when a phase loss is detected. So you only need to protect your motors.
A DC power supply that runs on three phase won't be affected much but the bridge rectifier can be overloaded and output ripple will increase. It will also attempt to pull more current through the remaining phase and blow a fuse or breaker. So again, its only dangerous to the load. If a 3 phase heater loses a phase, then guess what? You get less heat. That's it. Resistive heater loads can tolerate a phase loss with zero electrical problems. Your process will be affected but thats about it.
A three phase alternator does not care what the load balance on any of its phases is as long as they aren't overloaded. Same goes for a transformer. Many homes are ran off of a three phase 120/208 Y (sometimes spelled wye). Homes still get single phase 120/208 but are connected to the supply (phases A, B, C and Neutral) as follows:
The split is repeated for homes and they balance out the grid nicely. Splitting each of the three high voltage legs from a feeder into a neighborhood and stepping it down using center tapped 120/240 transformers makes balancing a problem. You can't interconnect any of the three separate 120/240 lines as the neutral or center taps must be grounded. Now you have 3 sets of 3 wires to deal with and you have to ensure you even distribute loads across three separate 120/240 supplies. Are you going to run 7-9 wires down a block to balance out that mess? No, of course not. So now you have individual blocks of 120/240 which may be unevenly loaded. Three phase is much easier as three houses in a row can easily balance out a 3 phase feeder. Both systems are used in residential neighborhoods (and at random might I add) but anything new is always three phase fed.
My home in Queens NY is serviced by a 120/240 center tapped 100kVA transformer that feeds only our street from corner to corner. The neutral connects to the other poles but everyone else in the surrounding area is on three phase. The poles do have 2400/4160 three phase feeders on top so getting three phase is not an issue. How we became a 120/240 island is beyond me but it might have been a leftover from old practices, never upgraded or left alone for a specific reason. Out on long island the neighborhood I lived in for a short while has 120/240 and only a single high voltage leg running along the pole. So they have to balance out the load on the feeder side.