Not to worry about that dirty, scummy tub, Yog!
What an ingenious idea Yogi--a bike basket-shaped filter for your multiple machines...
I could have just made do with a stand-pipe as that tub doesn't do anything more than just be a not-quite-a-bathtub but larger than your average sink that we do not use for any kind of washing in, (the valves for the faucets are increasingly hard to turn enough that if I were to get either/both to go on, it may be impossible to stop the flow shutting it/them off) but it doesn't leak!
So in short, I don't ever use it...
As for "a" stand-pipe, some friends of mine long ago with their radio dial Sears Kenmore had a self-cleaning filter (it boasted on the back-guard was how I got introduced to that features, and instantly knew it was to help eliminate lint) so I got to glimpse at the pipe with the u-notch at the bottom of it sticking out of the wall behind the washer, with the draining hose going right into it, in addition to the filling hoses, power supply for it & the gas dryer next to it, w/ the gas supply line likely to be down at the floor level behind the latter, while rising from it was the exhaust pipe for it going to a side wall, sticking out of the side of the house by the side door, that served the kitchen/utility area/laundry room...
Surely I would wonder and worry about that getting backed-up, and while combustable lint is flammable & hazardous for your dryer, washing machine lint & exiting water is just as much as a hazard (promoting water damage & flooding) as well...
-- Dave