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You want all 150 students in all your classes to come to your office every time you give out a homework assignment?A class with 150 students should have like 2 or 3 TA, preferably more, so the workload is split. If it's a obligatory homework, the profesor and the TA may have to grade it anyway. It it's optative homework, many students will not write it down, but it would be nice if all of them do it.
Checking an exercise in the first years of the university is easy. If it's correct, you must only check 3 or 4 key points. It's harder if it has a silly numerical mistake and you must propagate the error to see if the answer is "correct" or there are more hidden errors. Also, the important part is to identify why the student was wrong and try to get actionable advice, like study the rule of a derivative of a division, or study the rule of the multiplication of the signs, and perhaps add a 5 minute personalized class on the spot.
We have a list optative homework, and it would be nice if everyone do them. It would increase the workload a lot, so we would have to imagine how to solve that. In particular in a long list the profesor/TA doesn't have to check every exercise, only the ones the student had a difficult time or the ones the profesor know that are prone to error. If there are 10 integrals of polynomials and the first 2 and the last one are correct, the other 7 are probably correct too. In case there is an error, the advantage is that the profesor can explain one or two and ask the student to redo the other and come again later or another day.
The long list of exercises is useful, but in my opinion it's more helpful to write in the blackboard an additional optative homework each class. There are more solutions attempt than just leaving the list to be downloaded from the web page. (And it's easier to check because all the students are doing the same exercise. Also I can check if they are writing correctly the solution, sometimes the students get the correct result but don't explain the intermediate steps with enough details.)