Why are infected apps detected only after installation? Should the installation not be prevented?

For security reasons, the Android system does not provide any way to prevent the installation of some other app (which is usually a reasonable restriction). This is also an example of a fundamental difference between an Android smart phone and, say, a Windows desktop computer.
Nevertheless, MYAndroid Protection starts the scan immediately after the other app has been installed. There is currently no other way to provided this feature.
The situation is different when a (virus) app has not been directly installed from Google Play but has been downloaded elsewhere or was copied to the device's memory card via USB. In that case, the complete scan performed by MYAndroid Protection will find the virus even before the app is installed.