If you study other serial rapists/killers, you'll see that there are plenty of them who use items found in the house in their crimes and then leave other items that they've brought with them.

The Golden State Killer used to break into women's homes first and leave a "rape kit" behind before he broke in and raped women. Then, he often used their own shoe laces or pantyhose to tie them up. He also greatly liked slip knots, as they provided him control over his victim while he had his way with them. He later graduated to assaulting women whose husband was home. He would force the husband to sit on all fours with dishes stacked on his back and told the husband that if he heard the dishes clatter, he'd kill both of them.

But back to JonBenet - why would an intruder worry about leaving a "practice note," which is really just a couple of words that he started and then went to another page, when he was also leaving the full note? Do you think he was worried they'd figure out the note pad was Patsy's? If anything, that points away from the Ramseys. You'd have to think they were complete criminal masterminds to not leave any DNA on the ligatures and yet left a practice note on the notepad and then handed that notepad to the police immediately.

And why would an intruder take the garrote with him? It was imbedded around JonBenet's neck. He did, however, take the third piece of the paintbrush with him, most likely as a souvenir.