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Likewise. Mostly I use a router bit in a pillar drill with the feed locked - not entirely safe, but I'm more comfortable knowing the tool is fixed to the bench.
Most pillar drills have a Jacobs chuck in a morse taper, often without a drawbar, so the lateral forces and vibrations from an interrupted cut can unseat the chuck from the spindle.
You can get a router lift kit to mount a 1/4" trim router into your work surface. Attached example.
I find this too. I hardly use mine, partly for fear of injury.