It all depends on the situation and accessibility.
One hand probing would be highly recommended if probing in a cluttered device where you could easily bump your hand into something dangerous while probing circuitry that lies behind other conductors. It's especially risky when the conductors are corroded and you have to put a lot of force on your probes to pierce through the corrosion layer. Though, if you have to do this in the first place, it's a sign that device was designed in an unsafe way. And you'd be much better off getting a longer probe or probe extender, than just sticking one hand in and hoping the likely accidents won't hurt too much. If you really must do this kind of thing, see if you can get insulating gloves rated for whatever you're likely to encounter in there.
The one-hand rule is not, by itself, about doing things safely. It's about how to change risks you probably shouldn't be taking anyway from being likely lethal to being 'merely' quite painful injuries. It does become much better protection when combined with other safeties (insulating gloves, dry soil, insulating mat to stand on, rubber shoe soles... Those make it much safer by eliminating other current paths too).
There's always a balancing act when introducing inconvenient safety measures. Most safety features serve to reduce the severity of accidents. But if the safety measure is a nuisance, it might increase the odds of causing some other type of accident. Ever try using two probes in one hand, like chopsticks? Don't, very clumsy and likely to bump into the wrong things. The one-hand rule is a basic trick. It's better than nothing. But it's no substitute for thinking about what you're doing, thinking of alternative options to do the measurement, and considering the safety advantages and drawbacks of each. If you're working in such a hurry you can only depend on one quick rule of thumb like this, you're already going down a dangerous path.
If possible, the safer option is to power down (making sure no charge remains on any high voltage capacitors too), clip leads on, then power on. But this is time-consuming and requires cycling the power for each measurement. The one-hand rule is a compromise between safety and efficiency. It's a compromise you can't always afford to make: an example would be doing high-side current measurements on a high voltage power supply. Power it all down, put the multimeter, in current measurement mode, into the high side line. Place the meter on sufficiently thick insulators (also make sure all test leads are separated from anything grounded!). Put the meter on the right current range. Then turn the power on, and observe the display from a distance. You don't want to touch any part of the probes or the meter itself while doing this, don't even touch the range switch.