I've always read it that John the Baptist's preparing the way for Christ signaled a change in the earth. That is, that the kingdom which was once assumed under Israel's earthly rule was being manifested in a more personal way. Remembering that this was said in the general context of John's question from prison that expressed some doubt about who Israel was to look for. But more immediately, after Jesus had answered the question, the multitudes who heard the answer to John's question (which answer was "...blessed is he, whosoever shall not be offended in me.") were gently chastised by Jesus as He challenges their expectations :
And as they departed, Jesus began to say unto the multitudes concerning John, What went ye out into the wilderness to see? A reed shaken with the wind?
But what went ye out for to see? A man clothed in soft raiment? behold, they that wear soft clothing are in kings' houses.
But what went ye out for to see? A prophet? yea, I say unto you, and more than a prophet.
For this is he, of whom it is written, Behold, I send my messenger before thy face, which shall prepare thy way before thee.
Matthew 11:7-10
So there is some special significance to the appearing of John the Baptist. This is a man whose appearance signifies something different - something of a culmination. What culmination?
Verily I say unto you, Among them that are born of women there hath not risen a greater than John the Baptist: notwithstanding he that is least in the kingdom of heaven is greater than he.
And from the days of John the Baptist until now the kingdom of heaven suffereth violence, and the violent take it by force.
For all the prophets and the law prophesied until John.
And if ye will receive it, this is Elias, which was for to come.
Matthew 11:11-14
No longer was the Kingdom a matter of belonging to the nation of Israel - but it was that which "the violent take...by force". That indication of a violent one apparently has to do with one who presses hard to enter. Something which I think is illustrated in Luke's gospel :
And he went through the cities and villages, teaching, and journeying toward Jerusalem.
Then said one unto him, Lord, are there few that be saved? And he said unto them,
Strive to enter in at the strait gate: for many, I say unto you, will seek to enter in, and shall not be able.
When once the master of the house is risen up, and hath shut to the door, and ye begin to stand without, and to knock at the door, saying, Lord, Lord, open unto us; and he shall answer and say unto you, I know you not whence ye are:
Then shall ye begin to say, We have eaten and drunk in thy presence, and thou hast taught in our streets.
But he shall say, I tell you, I know you not whence ye are; depart from me, all ye workers of iniquity.
There shall be weeping and gnashing of teeth, when ye shall see Abraham, and Isaac, and Jacob, and all the prophets, in the kingdom of God, and you yourselves thrust out.
And they shall come from the east, and from the west, and from the north, and from the south, and shall sit down in the kingdom of God.
And, behold, there are last which shall be first, and there are first which shall be last.
Luke 13:23-30
The wording of this passage places this striving in the immediate context of Israel and the soon coming sending of the gospel to the rest of the world. The Kingdom would eventually be "given to a nation bearing the fruits thereof" (Matthew 21:43).
The Savior was constantly imploring those He came upon that the Kingdom was not a matter of racial or national membership but rather that it was to "come to them".
But if I cast out devils by the Spirit of God, then the kingdom of God is come unto you.
Matthew 12:28
The Kingdom of God in terms of rule and authority was all centred in Christ. So His appearing was the event that made it clear (or fulfilled for Israel) all that God was saying under the Old Covenant. That authority and power - that government in a metaphysical sense - was present on earth in the person and actions of Jesus Christ. And what was the response? Hostility.
Think not that I am come to send peace on earth: I came not to send peace, but a sword.
For I am come to set a man at variance against his father, and the daughter against her mother, and the daughter in law against her mother in law.
Matthew 10:34-35
So the violence the Kingdom suffers seems to be Jesus telling the people that they have been pointed to this Kingdom for generations - and now it is upon them. They do not naturally inherit the Kingdom (Jesus could make descendants of Abraham out of the rocks if He wished) but it is something they have to enter into - to receive.
He came unto his own, and his own received him not.
But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.
John 1:11-13
So the seeming paradox holds - one must enter into this Kingdom (it is personal, not national and is received only by those who meet the criteria of faith in God) but it is not something that man wrests for himself. In other words, only those that have believed the law and the prophets will even believe that He is the Christ. And those that believed were given power. But they also were not born of blood, the will of man or of the flesh - but of God. Isaiah's prophesying, then, to be done until the people were hearing but not understanding etc... was for this purpose. To weed out those born of God from those not born of God. Or in a temporal sense, to weed out those who had unbelieving hearts.
So when the Kingdom appears, those given that power will strive. Those who are born of God would believe and strive.