There are many stories of people who accepted salvation and were then immediately overcome by Holy Spirit and began speaking in tongues. But the fact of the matter is that it does not come that easy to most people. As with any spiritual gift, it requires stepping out in faith.
God will never be able to evangelize through you if you will not step out and share the gospel. One will never heal if they will not step and start laying hands on and/or praying for the sick. One will not be given prophesy if they are unwilling to step out and speak what they believe the Spirit has said.
Stepping out in faith is always risky business, but it is rewarded by God. I personally would not have known the gift of teaching if I had not had the faith to get up in front of a group of people and teach them. But I did it and God blessed me for it. The same goes for the gift of tongues.
If a person is waiting to be suddenly overcome by Holy Spirit at some random moment and start speaking in tongues, it is very likely never going to happen. That is why there are far more who say that they believe God "could" give the gift, but never experience it themselves. It is understood with the other gifts that there is an uncomfortable moment at first of stepping out, but with tongues they somehow think it is different.
It takes risk to start making sounds like "da da da bo da de" while praying for Holy Spirit to take over. It feels and sounds foolish to the mind. But if you really want the gift, you need to be willing to take captive those lies of the enemy (2 Cor 10.5) and step out with childlike faith, remembering that Jesus said, "...everyone who asks receives, and he who seeks finds, and to him who knocks it will be opened" (Mat 7.8).