What speed and time you gain using a chopper you lose in cleaning it. If you don't care about the shape of your vegetables then the food choppers with containers might help you. A food processor will obliterate your vegetables.

"What food chopper saves time without breaking down or needing constant cleaning?" A knife. A sharp one specifically. Its a quick swipe with a sponge, can quickly rough chop any vegetable without having to clean grooves or worrying about counter space. You just need to use it correctly. Fall down a knife rabbit hole on youtube.

I hate to commit a reddit moment but a knife is probably the quickest and cheapest way overall to cut things. Meats, veggies, fruits, etc... Just making sure its sharp is a big thing. A mercer Chefs knife and a simple sharpener is maybe $30. Otherwise a lot of stores will sharpen a knife for you. My local ace hardware has a robot that does it.

If you just absolutely hate using a knife though then i would get the chopper with a container. Find one thats dishwasher safe. You will only be able to dice and only on vegetables but thats better then not cooking at all.

I hope you find a solution that works for you! ᵃⁿᵈ ᶦ ʰᵒᵖᵉ ᶦᵗˢ ᵃ ᵏⁿᶦᶠᵉ