How to secure lock screen application for Android?

Question

Imagine the following case. Some lock screen application installed and configured on Android phone. Some pin or password set up. The app configured to be auto run after boot.

I checked this on Android 10. After phone reboot there is time window when OS loaded but lock screen app is not yet run. During this time phone is unlocked and can be normally used. In this period it is possible to just remove lock screen application and reboot without it and phone will be unlocked. When the lock screen app is started the screen gets locked (the time window is about 30 secs - 1 minute). I made 3 mins video with illustration of this behavior.

Is it possible to fix this because as I see all similar apps have such vulnerability? Or only stock Android screen lock setting is recommended to be used as reliable phone security lock?

I assume that this should be fixed on OS level by means of:

• Setting/option that will allow user to enter to the system after its reboot (swipe slider on first boot screen) only after all apps in the system will be run (when system and all its apps are fully started).

Am I right that such setting now is not exist? Are there some custom work arounds? Is it possible to prohibit removing some app (the lock screen app) or at least to hide it shortcut from desktop?

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Update 1. I have checked with another lock screen app ("Lock screen passcode" by "kunkun apps") on clean Android 7 on "Nexus 5" emulator. Got the same result. 5-mins video with illustration is here.