There's a really important lesson in all of this, offsets, and the visual segment of a non precision approach have to be thoroughly briefed, and there's no universal answer that fits every approach... Here's a few charts as discussion points:
IliasP, here is Tirana:
So, the offset really isn't huge in terms of direction, but the sideways displacement is more of an issue. It's perfectly fine to fly on the radial until hitting the minimums, you'll still have enough distance to correct. However, when I want to deviate from such a procedure early, even if its severe VMC, I still let tower know we have the runway in sight and we would like to continue visually, just to keep everybody on the same page.
TIA VOR 35
DLM RNP 19
So, here is Dalaman - and this is an example where you definitely shouldn't stay on the approach path until the MAPt if you're intending to land if you can help it, the offset is 15 degrees, and you will reach minimums three miles out - a nice distance to swing onto the centerline. Flying on the lateral path until the MAP reduces this alignment distance to 0.8 NM, so you'll be at perhaps 300 feet at this point. Why on earth they designed this approach that way is beyond me, there are no close-in obstacles on the centerline, and obviously they could have aligned the final part of the approach (at least after the terrain at BS116) with the runway if they wanted to. But alas.
TIV LOC Z 32
And for FlightDetent, here's Tivat - thankfully a clear case, it's charted with a visual segment, and the 20 degree offset and the terrain on the north eastern side doesn't leave you any room to turn onto final early. You probably won't be wings level by 500ft, 300ft is realistic.
Oh, and I'd just like to rant about the IAN feature on the 737s and now the 787 as well - there really should be an option to disable the "faux-ILS" indications on the PFD (apart from selecting an ILS frequency on the Nav radios), on offset approaches they are more distracting than helpful... I've had a first officer call LOCALISER repeatedly after I aligned with the centerline at DLM after the RNP 19 approach, bless him
