More than once I've read or heard people say their bearings weren't good enough for broaching on their milling machine. Wait a minute? Do you drill with your milling machine?
Okay, lets take a step back. Sure pushing a stepped cutter through a round hole to make a square or a hex takes a fair amount of force. I typically do that on an arbor press if I can. Its maybe not as much as people think though. Each tooth only takes off a little bit of metal. It might be an insane amount of force in a fairly thick piece of steel, but in most things we might be broaching is it really that much.
Still, I probably wouldn't do that sort of broaching on a milling machine. If for no other reason than you can't (or shouldn't) push the broach through the table below the part. Yes, there are work around methods depending on your ability to fixture the job, the available clearance, etc, but that sort of broaching is best done on some sort of a press.
Now here is where the cognitive dissonance comes in. A lot of broaching can be (is) done with a single tooth/flute tool, and engagement is easily adjusted to a suitable amount of force within the limits of the material being broached. Internal keyways are often done this way ona lathe. Lock the spindle and use the tool post to push through a cutter. Its not a high impact application unless the operator choose to make it one. A sharp tool cuts even alloy fairly well if you get the right amount of engagement. Sure a lathe headstock/spindle is typically more robust than a mill spindle, but its still axial force on the bearings.
So why not the mill? Old? Not as robust? Shock load? Maybe to all of those things, but for a single point/flute tool engagement is a choice. Its axial load which unless its total crap is the direction in which the bearings are strongest. How much axial load are you putting on those bearings when you are forcing a drill through a piece of steel? You know you have to push hard enough so it removes a chip, because way to many alloys will harden up on you and stop cutting if you don't.
In any case you have to do what you think is best, but maybe what is best is a little more nuanced than you think. Maybe think of broaching on the mill like using a clapped out old shaper. You are the one who chooses how hard the cut is.