1 Peter 3:15-17 doesn't make it sound like converting others on the spot is the point of having an answer.
Setting it up in vs 9 he says "Do not repay evil for evil or reviling for reviling, but on the contrary, bless, for to this you were called, that you may obtain a blessing." To me this pairs well with the appeal to be ready to give an answer with gentleness and respect in vs15
He follows with, "16having a good conscience, so that, when you are slandered, those who revile your good behavior in Christ may be put to shame."
Shame sounds harsh, but I don't think smashing the questioner is the point either...it would seem contradictory to the "gentleness and respect" mentioned in 15. Slander is like a fire(James 3:6). You can't put it out, it has to burn itself out. Either the target or the slanderer will be burned (put to shame). When you have a good answer, the emotion of the attack doesn't stick to you, it often continues to build in the accuser and he's the one gets defensive.
My take on it would be this: When aggressive questions or accusations come, the unprepared are embarrassed and ashamed. I would tend to get defensive and trade "reviling for reviling." When I lash out to protect myself I know I am acting in the flesh rather than the spirit and becoming a showcase a hypocritical lifestyle in front of a questioning unbeliever as well, this causes injury to my conscience and more shame. But, I find that the better prepared I am the less defensive I feel and the more capable I am of return and answer "with gentleness and respect."
Also, first phrase of 15 is "but in your hearts honor Christ the Lord as holy" or if you want to try and keep some of the original word order , "The Lord God, sanctify in your hearts" - when I am not defensive or lashing back I am able to keep the focus of my thoughts and speech honoring to the Lord. He can be set apart as first in my purpose rather than myself, who is where my focus is when I'm embarrassed and my conscience is injured.
Anywho, that would be my take on the purpose of having an answer. I don't think it's primarily an evangelistic tool, I think it's part of a holy lifestyle.