Mark 16:15 is only one verse of the New Testament, so there is much more to comprehend than that. The commandment of Matthew 28:18-20 shows that churches should preach the gospel, baptize those who are converted, and teach those who are converted & baptized. Evangelism is only a third of that equation.
I do not think it is necessarily his responsibility to disciple converts. However it is his responsibility to see that someone disciples them. That is why evangelists usually work with local churches.
Every evangelist or witness is not necessarily a good teacher of the whole Bible. But you are right. Working with the context of the local church, those who win converts have a responsibility to see that they are taught, not just left hanging in the wind. It's not unusual to see in reports of these independent evangelists numbers like 100 souls saved, 3 baptized. Something amiss there; and quite unlike New Testament evangelism.
Further, not having the "gift" of discipling can sometimes just be an excuse. If we try to teach/disciple others over the computer, we ought to have a little skill and responsibility to disciple them in person as well.