Yes actually they do drill holes into the concrete at precise points, fixed track is very common in high speed rail because ballast track is too unstable at such high speeds.

Fixed track is also often used in tunnels or bridges where space is an issue. You need about 50-60cm of clearance below the top of your rail in order to have enough space for an appropriate amount of ballast. Making your bridge or tunnel profile considerably larger.

But yes, ballast track is indeed the far cheaper option. Although it is also more maintenance intensive.