Yes. As I stated earlier, I run with anything. The Walmart stuff is my first time for car oil. I have used the diesel stuff. I quit the Mobil 1 and Amsoil because I paid so much for it, I was extending the drain interval. Synthetic oil gets dirty, too!
That sounds familiar.
That 2000 mile interval I mentioned was only exceeded once, when I splashed out on some Mobil 1 a few years ago. As the 2k interval came up I was keeping an eye on it and gauging the gearchange feel. Iirc, I got about 2500 miles out of that oil. The gearbox kills any oil that goes in there, even the best. I was tempted to keep it in for longer, simply because it wasn't cheap. The few hundred extra miles per change didn't justify the extra price.
However, I would have no hesitation on re-using the drained oil in an old snotter car, it's still got plenty of lubricity left in it, and the additive package is likely nowhere near used up.
Mineral oils start off as the 'w' rating as the base oil and the polymers are added to extend its viscosity range - synthetics are the other way around. Synthetics generally are the higher viscosity as the base oil, but are inherently multigraded and capable of flowing easily at low temperatures.
Either way, the gearbox chews them up and spits them out.
Just recalled, the shortest oil change interval I had was about 1700 miles from a 5w40 synthetic. It wasn't a name-brand, but got from Lidl as a car oil. I wasn't expecting miracles from it, but from 1500 miles onwards it didn't feel right, so it got dumped out.