It's just one element of Illustrator's inferior Bezier interface. Too many tool changes; too little functionality. In too many circumstances, you can't adjust one segment without wrecking the shape of the adjacent one. Related to this is the inability to bend a straight segment by dragging its middle, without introcucing an additional anchorPoint.

Remember the convert anchorPoint buttons in the Control Panel. Instead of switching to the Convert tool and dragging, you can select the anchorPoint(s), click the Convert to Curve button, then drag the unwanted handle back into the anchor. Be sure to have Snap To Points turned on, with a higher-than-default SnapToPoint tolerance set in Selection prefs.

Compare to FreeHand:

Convert one, several, or all selected anchorPoints at once. ((Illustrator still can't do all points of a path in one move.)

Choose whether to auto-extend or auto-retract the associated handles.

Click a button to extend / retract just the ingoing or outgoing handle(s), without worrying whether Snaps are on.

AltDrag to pull just one handle out of an anchor.

Bend a straight segment without changing tools.

Connector points to lock tangency between adjacent straight and curved segments.

Do all the above without changing tools; without need for two different selection pointers.

JET

HANDY TIP: When you got an anchor with it's handle connection broken or it's a point with only one handle and you want to convert back to a point with connected handles, snap a helper box (just a rect) to the handle point you want to maintain. Do your conversion. Then use your snapped helper box to snap the respective handle point back to it's previous, exact location.