Is there a reason not to put a beefy cap on the output of a homemade power supply?
The main reasons against are

inrush current
During startup, the capacitor effectively looks like a short to the power supply, so it will need to limit the current here.

&quot;higher-than&quot; requirements
The +5V rail might need to be kept above the +3.3V rail all the time, even during startup and shutdown. If you add large output capacitors and the +5V rail drops faster during shutdown, then the +3.3V capacitors need to be discharged into the +5V rail to protect any dual-supply ICs. If you have a large capacitor, this needs to be a fairly beefy diode.