I can only relate this to my experience of really preferring to wash my shorts every day, the saddle sore issue can occur and its just something I want to avoid.
I find washing them right away, getting as much water out by squeezing, let hang while doing shirt and socks, then squeeze lowest sections again, then use part of my towel to "roll and press" gets the most water out.
It's also so important to find the warmest and most open area for wind and sun to greatly reduce drying time. Bunched up overly wet clothes in the shade just won't dry quickly.
it's rare for my stuff not to be dry, but that's why a second pair of padded shorts is the way to go.
this is what works for me, everyone has to find what is ok for them to avoid having uncomfortable nether region issues that can be a real drag.
Yeh, just to be clear if it is easy to wash my shorts daily I do as well. If I have access to a sink or shower in camp my shorts get washed out too. If I wild camp a few days in a row they may not for that period.
As far as them being damp. I am soaked with sweat while riding most of the time, so I really don't see putting on shorts that are damp with water as a big issue. Sure I wring them out as best I can. I put them in the sun to dry too (inside out), but maybe more to kill what ever may start to live there if left too long. Sun is a great sanitizer.
Saddles sores or even just a bit of chafing can be a real problem if left untreated. I find that for me zinc oxide based diaper cream applied overnight works like magic, but doesn't work well while riding. In the morning and chafing that might have started is cleared up. During the day if any chafing should start one of the udder cremes used for milk cows works great. Some are packaged and sold for human usage and availble at big box stores drugstores, and grocery stores, but they are also available at farm supply stores.