The reason many people wash their car every week is to keep it looking nice and from the good old days of bad paint and no rust protection.
These days, paints are significantly better and stand up to some serious abuse, and the cars are much better rust proofed (galvanised etc...).
The washing your shirt analogy is a little unfair as with a dirty shirt and, you smell. A dirty car is just a fact of life... More like hiking boots, they're gonna get dirty at some point if you use them as intended. And likewise, to keep them in good condition, give them a good scrub every now and then... But like hiking boots, if you're using them every day then it's easier and more practical to just kick the clods of mud off and start walking again.
A reasonably modern car will be fine only being washed every month or so, if not longer if you don't mind a dirty car.
My personal preference is after the winter months, and there's no more salt on the road, jet wash all the wheel arches, suspension uprights, springs and everywhere you can get to underneath to really get it clean under there, and get all the salt out.
With two small kids, and being self employed-employed there's not enough time to wash the car every week (let alone every month!), and the interior gets a beating too... But it's a tool to be used, and hence will be getting dirty whilst being used. I've had nice cars, which are nice to keep clean and tidy but then sometimes you just need a workhorse - if the latter, then clean it as often as you want.
Edit to add: I live in the UK where they use tons of salt throughout the winter (we all drive on summer tyres all year round!), so corrosion is a huge problem on older cars - especially 80's and early 90's cars.