A full ILS approach adds about seven minutes to a straight in visual.
Not sure how you worked that one out. If you planned on a 'straight in', then you are going to follow the the same ground track as if you flew the ILS. The only time it is going to save is if you DON'T fly a straight in, i.e. you approach from any direction other then the extended localiser centreline.
In that case, if you shortened your route appropriately in the FMC, the most you are going to save is about 8-10nm from joining downwind and turning base to accomplish a 4nm final as opposed to flying all the way out to fly the ILS from about an 8nm final. In effect what you have done is shortened your cruise segment by descending earlier to be lower than the full ILS platform. Bearing in mind you will be doing something like 7nm/min in the cruise I think you can see that you will not save anything like 7 minutes by taking a visual.
If you planned on the full procedure and were offered a visual from abeam, you will be too high to just turn in so will end up going further downwind having slowed down and taken some flap and gear (earlier than normal to get the height off) and will be able to turn in earlier than for the full ILS, but the saving is going to be minimal.
Don't get me wrong, I'm all for appropriate visual approaches, but let's not exaggerate the true savings.
Sometimes the stated reason for a full ILS - Safety - is just an excuse to bring home more moolah at the end of the month.
Don't know what pilots you know, but I don't know ANY who would opt for a full procedure to get more pay! Even if you get duty pay by the hour, the extra minute or two is peanuts and most pilots would rather get on chocks quicker, get their post flight duties done earlier and get to the car park to get home quicker, especially after a long day........
PP