What conduit size to residential panel?
I have no idea what you're looking at, but no, the NEC does not demand a pipe that fat for a 200A feeder
I have absolutely nary a clue what sources you are looking at, but according to Chapter 9, Table 5A of the 2017 NEC, a 4/0 Al XHHW-2 compact stranded conductor takes up 176.3mm2 of fill.  Multiplying that by four, which is quite conservative as you will see, gives us 705.2mm2 of fill used by the entire feeder, whereas a 2&quot;, Schedule 80 PVC conduit has 742mm2 of usable fill area in it as per Chapter 9, Table 4 of the 2017 NEC.  So, clearly, a 2&quot; conduit will suffice according to the NEC; you can upsize to 2.5&quot; if you wish for ease of pulling, but no, you don't need to faff with reducers just to get your conduit to mate to your box.
Note that in all likelihood, you will not be running 4 4/0 wires for this.  The largest Mobile Home Feeder (MHF) quadruplex available is a 4/0-4/0-4/0-2/0, and there's also a 4/0-4/0-2/0-4 configuration available; while one could get 4/0-4/0-4/0-4/0 URD, there's no reason to given that Code permits a smaller ground wire and cables with the smaller ground wire are readily available in URD and MHF styles.  If you're actually pulling individual wires, a typical bundle would use 4/0 XHHW-2 Al wires for the hots and neutral, with a 6AWG bare or green (THHN) copper grounding wire in the conduit.