Well, I'm a chemistry tutor and I have a strong opinion about this because I've helped many frustrated students.
Honestly, I think online homework can be good and useful, however there are many websites that are difficult to navigate and input the correct answer, especially if chemical structures and reactions are required (like masteringchemistry.com). However I think masteringchemistry also has some of the best tutorials and conceptual exercises that I've seen.
I really think that the "homework" should be for only a small percent of the grade and that exams should be done in class for the majority of the lab. It's too easy for students to get together and cheat on their assignments or pay someone to help them.
I've even seen some online labs and those are really not very effective compared to a real wet lab.
What needs to be done is that the online material needs to be made more time-efficient and easy to navigate so I think multiple choice is the best way to go so that students don't get frustrated with inputting formulas. That's my 2 cents.