Part of it is the age, but part of it is that gas cars are designed to be driven. Letting them sit for any period of time will cause headaches. Electric cars should, in theory, be better in that regard as long as you leave them plugged in.
I'll speculate that things are failing on your Audi because it's an Audi, not because its gas powered. Go find someone driving a 15+ year old Lexus and ask them if something new breaks every time they drive. It's unlikely that they'll commiserate.
I'm actually buying a new (used) car right now. Around the $15k mark, I can get e.g. a 4 year old 7 seater that's done 60k miles. Based on my previous car ownership, I expect to spend around $700/year on average on maintenance, and around $1000/year on fuel. In total, I can expect a first year total cost of 700+1000+1500 = $3200 of which the biggest cost is a 10% depreciation. If I were to buy a $40k Model 3 (with less seats, less cargo capacity) that had 0 maintenance and 0 fuel cost, I'd still spend $4000 the first year to depreciation alone. 4000 > 3200. How are you saving anything?
Your argument can be applied to any new car. Buying used EVs will be the better deal, just like buying a used ICE is a better deal than a new one. Certainly the case for me. I've spent nothing on maintenance (except tires and wiper blades) and very little on fuel (electricity is equivalent to $1/gallon gasoline).