It is entirely unnecessary and IMO quite dangerous, to actually slow to a speed where full rudder can no longer control the aircrafts direction. For many common light twin trainers this will result in a speed very close to stalling speed.
Though I do not claim to be an expert in this, and am not an instructor, on the whole I don't agree with the generalization that the foregoing would be dangerous. It
could be dangerous, but then many things in a plane can be.
In flying at Vmc, not only
could you be very close to stalling speed, you could be right there. It is possible, and indeed considered favourable, that a twin reach stalling speed before directional control cannot be maintained with one engine inop.
I'm sure you are aware that the design requirements for these aircraft include: (my bold)
§ 3.123 One-engine-inoperative stalls. Multiengine airplanes shall not display any undue spinning tendency and shall be safely recoverable without applying power to the inoperative engine when stalled with:
(a) The critical engine inoperative,
(b) Flaps and landing gear retracted,
(c) The remaining engines operating at up to 75 percent of maximum continuous power, except that the power need not be greater than that at which the use of maximum control travel just holds the wings laterally level in approaching the stall. The operating engines may be throttled back during the recovery from the stall.
During recent flight testing I was doing in each of two Navajos, I was nervous about entering that phase of flight with the aircraft (both PA-31's, one with wing lockers, the other without). I am not well experienced in Navajos, and suffered from years of hearing hangar talk about how poorly they flew on one engine.
To the contrary, at both forward C of G gross weight, and light aft, I found these two Navajos, both with different external mods, to be very docile in this phase of flight. With the left engine both at idle, and stopped and feathered, and the right at 75% power, stalls were quite controllable.
On some occasions I reached Vmca first, and the stall was performed with either a slight heading change underway, or slightly reduced power on the right. Other times, I reached the stall first.
I have done similar flying in Cessna 300 twins, a King Air 200, and DHC-6, and found them to be similarly agreeable. I have not tried it in the light Piper twins, though the certification requirements would leave me expecting they would be equally compliant.
I agree that mishandling the aircraft can result in unexpected areobatics, and am empathetic to Big Piston's scare. I have found (first from some unsatisfactory experience in my poor briefing) that a very thorough ground briefing as to who will do what, and
what that will be, can be a great benifit to a no suprizes flight. I have occasion to be doing this type of flying in aircraft types I have never before flown, and sometimes in the company of other company or safety pilots. I have found that a complete review of the flight test plan [= lesson] (which takes 45 minutes to an hour), and the normal pre takeoff pilot briefing, tailored to the flight, are an excellent way to keep things safe.
In discussing what is to be flown, and what should be, but yet could be expected, everything is out in the open before you leave the ground. For any "newer" pilot reading this, who is in the midst of receiving instruction, do not try to truncate your instructor's ground briefing prior to a lesson. If your instructor requires a half hour of ground briefing, prior to an hour flight, eagerly pay the instructor for that time - particularly if you have questions, or something is new to you. You'll feel very much happier having spent the extra before hand, than having Big Pistons yell "I've got it" as you roll inverted in a Seneca after doing the wrong thing!