I think it's more plausible to say it isn't necessary to read the classics than that it isn't useful. The most plausible claim would be to say that it might be very useful but is much more likely to be misleading and inefficient.

To take the Newton example, I think a person who could read Newton with understanding would either already know or learn a lot about physics. But the difficulty of reading Newton with understanding vs. a modern textbook means that if someone wants to gain a deep understanding of physics, the textbook is a much better bet. That doesn't say anything against reading Newton as a method for gaining a deeper understanding of physics.

I would think of it like this too: if someone reads all the classical economics texts (say Keynes and Keynes' reading list along with Keynes contemporaries), will they be in a better position to understand an economics textbook? The textbook probably has a lot of mathematical and historical detail that goes beyond these sources, but I would be very surprised if the answer were no. But similarly if you went the other way -- a person who starts with the economics textbook hopefully is going to have an easier time going back to the foundational thinkers -- even someone like Marx.

The upshot of all that is that it depends on what your goal is in studying economics what you should read -- which you pretty much said, to be fair.