Water generally is less viscous than oil.
That may give the impression the oil has been produced, and it has, near the wellbore, but that leaves a lot of oil left in the reservoir. Horizontal wells will get that oil at a greater efficiency, but only when the well is drilled in the right part of the formation and produced correctly. Some things can't be rushed.
Another factor in apparent reservoir depletion is having reached bubble point, where natural gas dissolved in the oil comes out of solution in the reservoir rock, blocking pore throats and causing oil production to drop off. Maintaining reservoir pressure can prevent this, restoring it through injection of production water might cause the problem to clear up, but that is secondary recovery.
Often, what makes a well or field viable is economics: the cost of operating the wells plus the cost of disposing of produced water and cost of transporting oil to market versus the revenue generated by the oil, with costs for well maintenance and eventual site reclamation factored in.
If it won't make money, it will sit where it is, for the most part.
I did hear of an offshore well which gave the appearance of recharging, but it turned out the oil was coming from a deeper reservoir along either fault lines or fractures.
So, nope, no recharge, just the occasional rearrangement of fluids in badly produced reservoirs.
recharging is relative if one thinks in geologic time.
Unless for some reason the original charge stopped, there can be a very slow recharge component there.
since we use it up far faster, we cannot wait for geologic time to recharge, so for intents and purposes, it can be considered not a recharge situation, which is what I think you mean.