The problem is that there is no standardization in boards. You have got ICSE, CBSE, state boards, open boards, etc. Everyone has slightly different syllabus, different question patterns, and different ways of marking. ICSE is much tougher than CBSE, so same student will score less. So, unless everyone comes from the same boards, it is not possible to compare them based on their marks. So, and entrance test is necessary so that every student is judged based on the same questions and same conditions.
Another thing is that boards are subjective. Some students know a thing but can't explain in a better way, while some can write lengthy answers based on little fact. And some marks are even awarded for handwriting. Some good students have bad handwriting, which creates a bias in the examiner's mind. Objective test tests your intelligence and problem solving ability. Apply whatever method you like, you just have to solve the problem, which mimics real life scenarios. Your salary won't get deducted like your marks, if you don't follow the conventional method. In fact, one is encouraged to be different in real world, unlike the boards where everyone is supposed to write the same things and follow the same methods.
Another thing is board exams are much easier than entrance exams. It tests more of your rote memory rather than intelligence. i can't sya about other streams, but it is true for science. exams like JEE test how clear your concepts are and whether you can practically apply your theoretical knowledge to solve real problems. Boards just test how good can you mug your book and write word by word in your answer sheet. You may not understand a word, but if you can repeat what you read in the books, you score good. That's why you see many students scoring 90%+ in boards who can't clear JEE.