You don't always buy BTC on exchange service.
When somebody sells bitcoin to someone or buy goods or services to someone, then There is no exchange involve if this is done from paper wallets to paper wallets.
Authorities can start investigating from what exchange the BTC were bought from but can they say that all the wallets in which the BTC transited are owned by the original BTC user on the exchange?
if you buy bitcoin with euros and withdraw to address A
you move a->b
you move b->c
you move c->d
you move d->e
you can say that B was you buying something and B is a totally different person. meaning C, D and E should be left alone and not looked into.
meaning you think your safe at point C->
but if they see E was later linked to you depositing funds into an exchange or you bought something privately that linked to your home address. then all of a sudden A,B,C,D,E are all linked to you and any movements of any funds in the future related any way to ABCDE has some relation to you.
this is why people say only use an address once
for example
dont continually use C and D thinking only A and E are linked to your real life info
you move a->b
you move b->c
you move c->d x->d d->f
you move d->e
not only would they consider F is now linked to you too, they would also wonder who X was and why X paid you, and then check backwards at where X got their funds to pay you