Renting a car in Switzerland and taking it to Italy ... any suggestions for affordable rental car coverage?

All depends on your itinerary.
Will you finally drive back to Switzerland?

Yes, pick-up and drop-off are in Switzerland. Expedia is offering insurance for car rental at $13 a day but I cannot read any details - if it includes crossing border into Italy.

Who are you renting from?

Some credit cards offer a level of insurance on rental cars if you pay for the reservation and rental with that card. Not certain of the amounts, or if it's useful, and probably worth a phone call to the card company to clarify terms and coverage to see if it's what you are comfy with. I know that USBank and Chase cards offer this I'm sure many others do as well.

Few CCs provide insurance coverage for car rentals in Italy; checking the fine print is critical.

FWIW, to me, one of the joys of traveling in Switzerland is taking advantage of its excellent public transportation. It's so nice to be able to truly enjoy that breathtaking scenery! My understanding is that rail and bus connections between Switzerland and Italy are also quite good. So, while I know that we all travel with different preferences, I wonder if the OP has considering eschewing the rental car. For info about public transportation in Switzerland, https://www.sbb.ch/en; for cross border options, rome2rio.com (making sure to click through to the underyling links).

Thank you for the information. I decided to purchase the Expedia insurance and also put it on my Chase cc.
I did make some phone calls but a lot of times you are talking to some agent in Wichita or Manila who really has no idea about the fine print in foreign countries 3000 miles away.

Chase reserve used to cover Italy. Not sure if it still does. Won’t cover you however since you bought a separate insurance. I always just buy coverage through Auto Europe for Italy rentals.

Many credit cards do include rental car coverage when the contract is paid using the cc, depending on the country. However almost NO cc's offer coverage in Italy. A few that used to no longer offer it. And one or two that currently cover Italy are closed to new 'members'. This complicates renting cars when some driving is in a 'covered' country, and some is in a 'non-covered' country. (Same applies to Ireland and Israel BTW - the 3 countries are special cases)

If it were me I would take trains and public transport and relax!

Obviously the trains would be a great option except A) it's significantly more expensive and B) it doesn't offer the flexibility needed in places like the Dolomites.