It is unlikely in the extreme that an opening door on a certified airplane is going to create a controllability/safety of flight concern. Airplane designers have errant opening doors in mind during the design process. That's not to encourage carelessness on the pilot's part, but rather to remind pilots that their first responsibility is to fly the plane safely, and keep flying it, until it's safely parked. Everything else is secondary. If a door has popped open, and once safely airborne, you'd like to close it, before applying silly amounts of pull on the handle, try some rudder one way or the other. The jump planes I flew with air operable doors were very easily gently opened and closed with rudder operation. If the door has an opening window (Cessna style, not the Piper hole in the window window), open the window, and pull on the lower aft portion of the window frame, it's stronger than the handle, and closing the window later is easy.
Many airplane types are permitted flight with a door removed, though often by additional approval, and sometimes with a deflector. A partial list for interest's sake includes most Beech Twins, All the Cessna singles, and a couple of twins, Most of the Piper PA series singles (though the Tomahawk does not appear on the list), and a number of other types.
If you're flying a Cessna Caravan solo, remember to lock the back cabin door from the inside (not just "closed and latched"), they can open in flight if not completely locked
. Not harmful, just embarrassing. If you're flying a single Cessna with a baggage door, key lock it before takeoff, their latches are mediocre. The only type which I know sustains expensive damage with an errant open door in flight is the C 206/207, if a back clamshell door opens. It'll bang on the side of the fuselage and beat it up. The plane is safe to fly, but if it happens, you'd better continue on to a maintenance base, 'cause the plane is going to need repair before the next flight!
For GA singles, emergency crews are going to get in. I agree that there are flight manuals which state to unlatch doors before a forced landing - then you should certainly consider doing that, it was written for a reason. Otherwise, close them properly. Note that a few types (I'm thinking of the Cessna 177's) have a number of moving pins which latch the door closed in several places around the frame. These are moved into place in the motion of the handle from "Closed" to "Latched". If that motion of the the handle is not easy, reclose the door, as one of those pins may not have gone into position properly. If you force the handle to the "Latched" position, a pin may hang up, and spring a bit. Later in the flight, particularly in turbulence, it may pop into the correct position - it'll scare the @#!* out of you!