is this simulator realistic for a Cessna 172P?
Fairly - my brother (aerospace engineer, trained on a C-172p) claimed that the FG version has a little too much power, but otherwise feels about right.
There's likely planes with even better flight dynamics (generally where we have more data) - the Saab Viggen for instance is based on a ton of real data, it behaves like the real thing even in pretty off-nominal attitudes.
Meaning... if someone stuck me in a Cessna 172P, assuming everything was okay with the plane, would I be able to take off and land a real life airplane if I am awesome at flying in FlightGear
Had to say - I was able to fly and land my brother's aircraft (a Diamond, don't ask which version precisely) based on some familiarity with it in FG, but I am also trained as a real-life glider pilot, so I know the basics of flight.
the flight model has it's flawes, the most noticeable one being the oversensitive elevator
I'd generally be careful to pin down oversensitive control X on FG. The feel of a real aircraft control is not really matched in any way by most hardware you can put on your desktop.
In the gliders I've been flying, you have a direct link to the control surfaces from the stick, so you have airspeed dependent stick forces and very little deadband, so flying straight is a constant series of minute near-subconscious adjustments. I get some of that feeling with the better JSBSim planes and the mouse (which has a similar degree of fine sensitivity), but you'd need a fairly sophisticated hardware to provide the full experience.
The Diamond on the other hand surprised me by having really hard stick forces - it wanted to be commanded, not carefully steered, so I tended to provide to little control input.
In most situations in a glider, I would never pull the stick full back (or even half) - there's LOTS of room for emergency maneuvering and aerobatics. The force feedback would of course make this a self- ending process, you don't easily pull too much. So dependent on how your computer hardware is set up and configured, if that outputs full deflection fairly regularly, you'll find controls overly sensitive while the FDM is perfectly okay.
In fact, flying with the mouse, I do get this behavior, because usually I hardly move my hand and make very minute adjustments ( a mm of mouse motion perhaps) - but of course if I steer with large movements (a few cm motion) the planes over-react quite drastically.
So I suspect in many cases overly sensitive controls are not baked into the FDM but rather have to do with control HW calibration and usage.