Unless the defense atty is ready to go to trial, ASAP, s/he will always waive speedy trial.
It would be malpractice for an atty to rush to trial, unprepared. For you, that could be disastrous; for the atty, extremely embarrassing and possibly a reason for your anger.
Most attys will waive speedy trial, 45 days at a time. If the defendant was out of custody, the People have 45 days from the arraignment & plea, to bring the case to trial; if the D is in custody, then it's 30 days to trial.
Most defense attys, at the arraignment and plea, haven't even received the discovery (the complaint [charging document] & D's rap sheet & any proof/evidence booked) until that day. They are usually, in court, trying to read the charges, get an offer from the Prosecutor, plead their client not guilty, & waive time to the next appearance.
In many jurisdictions, if the defense atty doesn't waive time, the Prosecutor will not make an offer (plea bargain) on the case (because if subpoenas have to go out and witnesses are called into court, why make it easy on the D ? As long as subs go out, may as well do a quick trial.)
So, no, your atty can't advise you of every right, immediately.
If time was waived, it was done on a 45 day period, only.
If there was a repetitive waiver of speedy trial for a lengthy period which you never agreed to, then it may be malpractice. But waiving trial is a common practice of def attys who are always hoping witnesses die, retire or get transferred.
So, it may prove to be wise tactics in some cases.