This is a very difficult problem. If the sanitary sewers aren't in great condition, rising ground water levels can leak into the sanitary sewers. Sewers that were initially well made might be damaged over time by people digging, the ground shifting, or tree roots pushing things around. One way or the other, when high ground waters get into a sanitary sewer, you now have a situation where those sewers are overflowing. And what can be done with that overflow? Let it pool up in the streets? Sending it down the storm drains is about the best you can do at that point.
There is no easy solution to this. Building the sanitary sewers bigger is the obvious solution, except that costs more money and a lot of places don't have much money to spare (corruption, poverty, etc.) Furthermore, just how over-designed does a sanitary sewer have to be? Climate change makes this difficult to predict decades in advance.
BTW [intentionally] combined sewers are problematic even when they're not overflowing. Diluting sewage with a bunch of water increases the cost and decreases the efficacy of treatment.
Combined sewers are definitely problematic, but if diluting costs more depends on the inputs to the treatment plant. Some plants need to dilute with fresh water, and storm sewers are freshish, so it might reduce costs to use storm water rather than potable water.
If all else is equal, in my mind, I'd run the storm sewer to the treatment plant and treat it when there's capacity and let it flow when there isn't. Of course, most of the seasonal difference in sewage flow is from groundwater infiltration, so that probably doesn't make a lot of sense... Both systems will be at higher flows at the same time, for the most part.