LTSpice power supply simulation: what is wrong with it?
It looks like you're trying to provide about 15 V to a 6 ohm load.  Unless I misunderstand your schematic...  So that's 2.5 A.

Now consider that the diodes only turn on and pull current from the AC source about 1/5 of the time (only when the 23 V sin goes above the 20 V or whatever rectified voltage you're getting).

In order to average 2.5 A (plus whatever is sloshed in the the parallel caps) at 20% duty, you'll need to average about 12.5 A during that 20% of the time.  So, a max of 16 A doesn't seem unreasonable to me.