Well, to be exact, it isn't always ineffective - indeed, conservative evangelical protestants are among very few denominations still winning converts among native European-descended people. But the numbers are small, and most Westerners are immune to their message.
Why? Because traditional Christian evangelism focuses on salvation - on saving-from Hell. (Note: All the following is true, and I endorse it...) Traditional evangelism focuses on sin, and the need for repentance from sin. It focuses on getting people to recognise their sins, acknowledging that sin really is sin; and on having faith in Jesus as Saviour - in understanding that faith in Jesus is both necessary and sufficient for salvation.
All of the above is true and necessary and absolutely-must be affirmed by all Christians - and yet it doesn't work.
It doesn't work because people don't believe God - consequently they don't believe in the reality and objectivity of sin, they don't believe in Heaven, so they don't believe in Hell... even worse, they prefer Hell to Heaven; because Heaven would entail giving-up some favourite (usually sexual, but maybe emotional) sin. It doesn't work because people don't feel the need to be-saved; and they are unimpressed/ uninterested by what they are being saved-for.
And it doesn't work because the primary suffering experience of modern people is alienation - of being cut-off from the world; of finding life (meaning this mortal life) meaningless and purposeless: of finding nothing really-real, and of being haunted by a conviction that life is merely a senseless and lonely spark in eternity.
To save someone from alienation is not like saving someone from the consequences of sin; saving from alienation requires, more than anything, a purpose for life. From that purpose can come meaning, and that purpose may also give meaning to relationships; and when that purpose extends beyond biological death then a great deal has been achieved.
Christianity as a faith has, so far, been bad at providing positive purpose. Instead, purpose has traditionally been provided not by the faith but by the church, by the human organisation. Yet most Christian churches are now corrupt, and indeed anti-Christian overall; and those which are not corrupt are small, scattered; and mostly incapable (through lack of persons and resources) of providing an 'alternative purposive life' for alienated moderns.
What is needed, then, is development of Christian doctrine that goes beyond salvation; moves directly from saving-from on to living-for; from the negative to the positive.
I think this means Christianity picking-up from the incomplete 'project' of Romanticism - as exemplified by Blake and Coleridge; of seeking to reconnect Man with a living nature, of recognising that God is within as well an an external person, of thinking much more about the nature of Heaven than the avoidance of Hell. And understanding Heaven as an active, dynamic, purposive world - a world of loving relationships united in divinely creative activity.
And recognising that this is something we can, and should, be doing here and now, on earth, during mortal life.
This is the Good News of Christianity for moderns; and ought to be the first point of contact and primary message. Salvation is absolutely-necessary; but it is a means and not the end. As it says in the Fourth Gospel (John 20:31):
...these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name.
Which makes clear that the ultimate purpose is 'life', which (through this Gospel) means the divine, Heavenly consciousness.
Even knowing this; not everybody will even want life everlasting, life more abundantly, the life of Sons of God - most of Jesus's audience rejected it, after all. But modern people ought to be clear, at least, the magnitude of what it is they are rejecting.
If they can first understand the nature and scope of what is positively 'on offer' - only then, and if they want it, they can then decide whether or not this offer is real and possible.