I know you're not supposed to rectify mains because it's "dangerous" but if I use a 1:1 transformer and ground it to earth how exactly am I any "safer"? I ask because it would save me $130 to simply rectify mains and get the same voltage.
What you are describing is an isolation transformer.
Since the mains lines are referenced to real ground, touching one wire with your feet or other hand electrically connected to ground completes a circuit with YOU in it. That tends to spoil your day.
If used properly, an isolation transformer isolates the power lines from the ground. As such, touching the live wire on the isolated side while touching ground with your other hand does not complete a circuit.
Of course, none of that matters if you touch both sides of the power on the isolated side.
If you end up grounding one side of the isolated side of the transformer, you make that situation worse. In fact, in that case you are in more danger than touching the primary side which should be protected by an "earth leakage" or "ground fault" circuit breaker. Unfortunately, an isolation transformer takes those out of the circuit.
The transformer does however limit how much current can be passed since it will saturate at some point. That is better than connecting your self direct to the multi-megaWatt grid.
Because you get isolation with a transformer. The insulation of the line shields you from the full current that the mains line can source. Since transformers usually have a magnetic core, this also saturates and can help limit current. Why would you want to limit current? In the event of a short.
So yes, because of isolation and current limiting a transformer is safer.
In many cases the transformer isn't just a good idea, it's required.
Because of the isolation, the secondary is floating. You can still reference your circuit to another voltage, like ground and get the power limiting of the transformer.
Source: Learn about Electronics
If you're going to ground one side of the transformer secondary, then you're no better off safety-wise.
However, with a transformer, you can ground the negative side of the full wave bridge output instead. Now you have one side of the supply that is safe. The other still has dangerous voltage, but that will always be the case whenever you have such high voltage.
If you don't really need rectified line voltage, then you can have the transformer serve two purposes: Provide isolation and reduce the voltage to a safe level.
Either way, you have to start by thinking carefully about how the DC supply will be used. Will it be totally internal to the unit and well insulated from the outside? If so, no isolation may be required. Will its ground need to be connected to external ground or something the user can touch? If so you probably do need isolation.
Now we have the context that this is a valve amplifier it is possible to give a more useful answer.
In normal equipment both the mains live and mains neutral need to be regarded as hazardous. Even if your country reliably connects neutral to earth and uses polarised plugs there is still the worry of what happens if a wire breaks or a pin makes bad contact and the worry that volt drop in the neutral wiring can drive current where you don't want it to go.
We also must avoid too much leakage between live/neutral and earth since it would cause hazards in the event of a lost earth.
A valve amplifier generally has at least one connection to/from the outside world. These connections need to be safe to touch and they need to be referenced to one side of the supply. So we require one side of our power supply to be touch-safe. Normally this is achieved by using a transformer and than grounding one side of the rectifier output.