Waiving rights is weird. It’s well understood that you can’t waive your right not to be a slave, for example. Why should you be able to waive any right? The 6th amendment doesn’t say “unless the accused doesn’t want it.”
Because it's presumably beneficial. It gives your lawyers extra time to prepare for the case or to potentially settle on more favorable terms.
You can waive your right not to be a slave, but no one can gain the right to legally own slaves. The 13th amendment doesn't guarantee the rights of people to live free, it bans the practice of slavery. If you find someone living in slavery you don't arrest them for being a slave, you arrest the person who enslaved them. If someone asks you to do something illegal for them, you are obliged to say no; even if they are the only person directly impacted and they insist they want it, it is not in your authority to grant the request.
You can choose not to exercise any right, that's what makes it a right. Freedom of religion does not imply an obligation to practice religion, freedom of speech does not compel speech, right to bear arms does not imply an obligation to bear arms, etc. Your right to a swift and speedy trial is likewise something you can choose not to exercise. Things would be different if the law was all trials must be swift and speedy.