The biggest rodeo ride in a small SEP may be a typical Mooney, which will really dramatically lower the nose on setting flaps. On the opposite, when getting flaps in from take-off setting a Mooney will shoot straight up like holy toledo.
Well, maybe not
straight up.....
Let's remind ourselves that the certification requirements for which the Cherokee series, and all Mooneys would have been found to be compliant would read:
(b) During each of the controllability demonstrations outlined below it shall not require a change in the trim control or the exertion of more control force than can be readily applied with one hand for a short period. Each maneuver shall be performed with the landing gear extended.
(1) With power off, flaps retracted, and the airplane trimmed as prescribed in paragraph (a)(2) of this section, the flaps shall be extended as rapidly as possible while maintaining the air speed at approximately 40 percent above the instantaneous value of the stalling speed.
(2) Same as subparagraph (1) of this paragraph, except the flaps shall be initially extended and the airplane trimmed as prescribed in paragraph (a)(2) of this section, then the flaps shall be retracted as rapidly as possible.
(3) Same as subparagraph (2) of this paragraph, except maximum continuous power shall be used.
(4) With power off, the flaps retracted, and the airplane trimmed as prescribed in paragraph (a)(2) of this section, take-off power shall be applied quickly while the same air speed is maintained.
(5) Same as subparagraph (4) of this paragraph, except with the flaps extended.
(6) With power off, flaps extended, and the airplane trimmed as prescribed in paragraph (a)(2) of this section, air speeds within the range of 1.1 Vs1 to 1.7 Vs1 or Vf whichever is the lesser, shall be obtained and maintained.
(c) It shall be possible without the use of exceptional piloting skill to maintain essentially level flight when flap retraction from any position is initiated during steady horizontal flight at 1.1 Vs1 with simultaneous application of not more than maximum continuous power.
So there can be pitch force changes, but none such that an attentive pilot would have difficulty controlling.
the opposite is not less uncommon
Which is something like: "it's getting less worse more slowly."