Why must they? If the prosecution were to not introduce them and the defense were to not introduce them they they would not have to put into evidence. If the prosecution does not and the defense does, then the defense has cut off some objections it could make at trial and some grounds of appeals it could mount on any conviction. To me that is an unnecessary risk when you have an affirmative defense.
Suppose a different situation--your client is accused of robbing somebody based off a bystander recognizing them. A witness then comes forward that says she saw your client at the mall and talked to them for a period of time which was the same time that the robbery was committed. Would you want the fate of your client decided upon who the jury believes is telling the truth between the two, or would you want your client to testify affirmatively "I was at the mall"? Do you not think it reasonable that your client's refusal to testify could be interpreted as evidence that your witness was maybe lying for a friend and therefore your client is guilty when you client may have been at the mall and the witness just misidentified them?
Two entirely different sets of questions.
You are correct the defense can not object to evidence it offers generally. The defense COULD object to a tape, but then if the prosecution cherry picks it object to it not all being shown - without thereby waiving the initial objection to the tape or tapes themselves. The reality is the prosecution is going to put on the tape(s) of GZ acknowledging his shooting TM - and ultimately will try to use various inconsistencies among all the tapes to impeach GZ.
GZ's case is different in that it is very rare to have SO much footage of a Defendant telling his side - to the police, on video, in police interrogations and even to the media.
As for your second question? Whether a defendant goes on the stand or not is very complex given how truly bizarre the US legal system is in allowing attorneys on both sides to make any accusations, essentially state any lies in the form of a question, and overall abuse and harass the hell out of a witness - with it so strictly held to Q&A on behalf of the legaleze of the lawyers as if it all only exists for them that most judges will rage at a witness or defendant on the stand trying to tell their side outright.
The other problem is the EXTREME imbalance between prosecution and defense - favoring prosecution. The prosecution is on record of wanting to put witnesses negative to GZ's character on the stand. Yet if so, 100% of anyone who ever heard or saw GZ do anything in his life should also be witnesses for the defense. If ONE witness of the prosecution testified that GZ used a racial slur, the defense should be able to put on 1,000 people to testify that they never heard him do so. If one woman testifies he was abusing, any woman he ever dated should be then testifying also whether or not he was. Of course, only the very wealthy can put up an equal fight - particularly since in this case the prosecution had and essentially has unlimited budget and staff - and GZ is just a poor below average intelligence ordinary person.
Whether or not to put a defendant on the stand is likely often a very difficult question.
Since I do not agree to many of the tenants jurors have to swear they would follow, I will never be on a jury. I would absolutely willing to totally disregard any law I felt wrong or wrongly being applied nor care how a judge told me to consider the case. I think the core purpose of a jury originally was to be a check against government excesses or injustices - not the employees of the government court as jurors are now required to swear they will be.
I also have VERY strong views about violent conflicts between men. If both proactively got into it - and both TM and GZ did - however it ends is however it ends. To often trials get into unreal and contrary to human nature trying to micro analyse what happened to some standards of perfection, rather than the extremely limited intelligence, intensely emotionals and highly instinctive natures humans really are.
FROM BOTH DIRECTIONS...
If it happened this way coming from TM's perspective, if some guy was coming threateningly and I saw he had a gun and was going for it, I absolutely would beat that person into the ground regardless of what or who "started it" (and in all likelihood could given all the men I did beat into the ground in the past).
OR, from GZ's perspective, if it were to happen that some guy got me on the ground and was beating the crap out of me, again regardless of who or what started it, if I had a gun or could get my hand on one I would definitely shoot that person.
Therefore, once the forensics showed the shot fired at essentially point-blank range (wasn't a distance execution or shooting while TM fled), I'm ok with what happens as just what happens between men/males who get into a violent conflict they both walked into. If, instead, it was GZ dead, my opinion would be exactly the same.
I've seen so many truly innocent people hurt during my early life nor did anyone ever feel sorry for me or come to my rescue, that ever since if two fools or aggressive acting men/males get into a violent conflict then however it turns out is however it turns out. Don't go crying to the government, cops and taxpayers to do anything about how it turned out. BOTH TM and GZ 100% could have avoided this. They didn't. They BOTH walked right into it.
So... asking what I think maybe will not produce "normal" answers.