Some modern Christian evangelism is working, and should be continued; but the signs are in the direction of declining effectiveness.
This may be because modern Western people are living in a secular and anti-Christian environment; plus they are also, by their innate nature, resistant to the necessary step of consciously and by free choice becoming Christians.
This modern West is a society in which evil primarily (not exclusively) takes an Ahrimanic form: meaning that it is systematic, procedural, dry, cold, bureaucratic... and aims at a totalitarian world of omni-surveillance and micro-control of human behaviour; including (it is intended) human thinking.
By my understanding; this means that Christian evangelism will Fail insofar as it approximates the bureaucratic nature of modern evil. That is, evangelism will fail, or be counter-productive, insofar as evangelical efforts are a system, a set of procedures or guidelines, based upon managerial structures, treat individuals as inter-changeable units and resources etc.
What lies beyond the Ahrimanic tendencies of the modern age? Well, one aspect is that it is a world of acknowledged individualism, freedom and consciousness. Evangelism is therefore a matter between two individuals, an encounter of chosen mutual willingness; and an encounter of 'heart-thinking, intuition, and a knowledge which is direct and also conscious.
In a world where manipulation of persons by subliminal messages, lust, pride, fear and resentment are the norm - these must all be eschewed. Christianity needs to be presented as what it is, in a positive and without-using-threats way - as the potential object of a positive choice... And not, therefore, a choice imposed by fear of the alternatives and the desire to escape them, nor a choice presented as the only possible coherent solution to a philosophical problem.
Some-how (and this may well be unique per person, to be known only by direct and individual human engagement) the hope is to present the Christian vision of life as-a-whole and with its wonderful possibilities... then to step back and say (in effect):
"If this is what you want, you should discover whether (or no) there is significant reason to accept that the Christian promise is both true and possible.
"If you want it and there is significant reason to believe it possible, then it is rational to choose to believe it.
"And you need to make that decision."
And the choice-to-believe then opens-up the many other possibilities; including faith - which is that loving trust a child feels for his parents in an ideal family.