Attila

The idea is not to disturb the roots too much. Late spring is still accepable to repot, but not the best time. Especially with weakened trees.

I would lift the tree out of the pot (if it's tied to the pot with wire, cut the wire first at the drainage hole, if not, just lift it) and see how rootbound it is.

If the soil is lose, just shake it until half of it falls off. At this point, if you see lots of dead black roots at the extremities, cut them off (not more than 20 - 25% of the total rootball)

If the tree is so rootbound that the shape of the rootball is following the shape of the pot, and it's a compact mass of roots, with a hook carefully comb out the outer portion of the rootball and cut off about 20% of it.

To answer your question, the problem with replacing all the old soil is that in order to do that you may have to disturb the roots too much, and that's not good.
However, if you can just shake it out without too much disturbance, it's for the better.

After repotting, it's very important to place the tree in light shade, protected from noon and afternoon sun. At the beginning, you may notice that some of the old leaves start browning at the edges, but soon there will be new growth coming out.