Because version 60.1 is still rolling out. Your device’s manufacturer (Samsung, OnePlus, etc.) may also delay Google Play System Updates.
Samsung, Xiaomi, OnePlus, and others often modify Android deeply. Consequently, they may be slow to certify and push Play Services updates. Manual installation lets you take control.
Go to Settings → Security → Install unknown apps and allow your file manager or browser. Remember to turn this off after installation.
There are only two specific reasons anyone should download Google Play Services 6.0.1 APK:
Yes. Version 60.1 officially supports Android 9 through Android 15 (current beta).
Cybercriminals frequently package spyware or banking trojans (like EventBot or Hydra) into fake "Google Play Services" APKs. Once installed, they can intercept 2FA codes.