I use conventional oil in my NA Z cars, but that's simply because I'm cheap. If I paid over 3k for one or rebuilt an engine myself I'd consider running synthetic. For a completely stock L motor I just don't see the point. Now, my current DD is a 280zx that I got with 200k on it and BAD oil burning on engine braking and even keeping it in neutral while braking I'd still go through almost a quart every 500mi. So my cheap ass started putting in 20-50w. I've received flack for that here but guess what? The engine now has 245k, runs as good if not better than when I got it, and has no indication of getting worse. Is this from my oil choice? No, but I'm pointing out that oil weight is only a small aspect of engine health.
In a perfect world I'd figure out if its a leak in the head or rings, and just fix it. But why would I do all that on a car that's been fine for over 40k that I got for FREE???
Now, my turbo motor always gets synthetic and I run 10-30w. But I'm a firm believer in synthetic for turbo motors and choose weight base more off of what temps are where I live than anything else. Also, I add a zinc additive in most cases because most oils are low on zinc since it's no longer as needed in modern engines. But I'll be the first to admit that's more of a "well it can't be bad so why not?" kind of thing.