I think they are fairly well-designed. You have to be able to expel solids and liquids somehow, otherwise they'd build up inside you, and you might die if they couldn't be digested or sweated out. I guess they could be combined, like birds. But I don't think that would make it less 'gross' in a non-quantifiable way. Sweating is also a pretty effective way of cooling down. Other methods such as large ears as radiators, thin blood vessels on the forearms that must be licked to aid in heat transfer, and panting all have their downsides.
If you think about it, tailpipes on cars and vapor pipes on AC and heatpumps and furnaces are basically the same thing as our digestive system.
The only thing that could really be redesigned is to have them be much more efficient, like some animals, which can pull a lot more water and nutrients out of byproducts. That, and the ability to extract stuff like heavy metals, microplastics, and forever chemicals, which get stuck and can't always leave.
Waste does not have to leave residue behind and stink. We ought to be able to extract more nutrients from digestion, and we could probably make an implant to carbonize waste, compress it into pellets, and even wrap it in a biodegradable capsule before disposal. I do like your point of dealing with hazardous materials.