Rats are actually very clean and groom themselves constantly! I'd give mine little baths and they'd just sit there all spooked up waiting for it to be over lol
They can also be potty trained though males are easier than females so you better be ok with giant nuts being dragged around your place.
It's a mating strategy as sperm volume increases the rat's chance to reproduce. Single female mates with multiple males and more volume translates into higher chance for male's sperm to succeed.
In general, nut size directly correlates with promiscuity across most species so you can tell how a species fucks just by looking at their balls :D
Nothing that lives in sewage is clean, least not the things that clean themselves with their mouths. What makes something unclean is not dirt, it's the pathogens.