Yes, deeper cuts mean more force on the cutter, especially in that split second when the cutter has just finished the vertical plunge (so it does not see any lateral force at that point), and starts moving along the profile cut, at full depth: all of a sudden there is a large resistance, enough to make a small tool deflect just a little bit.
@LiamN’s tip is a (great) variation of the “roughing then finishing” approach, indeed a single pass at full depth with a compression bit after the profile has been roughed will leave very clean edges at the top and bottom.
Carbide Create does not (yet?) have a function for automating the creation of roughing then finishing toolpaths, but you can emulate it with creating extra geometry like Will explained in that article. Short version: create an additional profile, offset from the final one you want to cut by say 0.5mm. Do a normal profile cut on that offset profile, using your regular cutting parameters (probably limiting depth per pass to a fraction of the cutter diameter). Then create a second toolpath, the final/finishing one, by selecting the original profile, but this time there is so little material left to shave off (0.5mm all around) that you can afford to define depth per pass as being the total depth, i.e. go around your part in a single pass.
Other CAM software packages have built-in parameters to do the same, it’s essentially the same idea but they just spare you the effort of creating the extra geometry explicitly. It’s “only” a productivity thing.