Devs it is really annoying when testing your game etc. and it suddenly crashes that hole unity crashes which leads to not knowing what caused it. Why your game not run like an app in visual studio if your app crashes there the app is stopped or you can close the app window and get the error in your console. This would be really handy for debugging because i've crashed unity a lot of times now often just out of nowhere not knowing what caused it. Do you understand what i mean? Like the game would run inside unity with unity as the overhead.
The reason why it is not stand alone app is, because is strictly integrated with the Unity editor. You can interact directly with GameObjects and many Unity tools at runtime. For stand alone version you got build. And there is crash reporting tool. But I get the reason for your pain. If ever happens to me, I then tend to check out last changes I did and see, what may be causing crashes.
You can attach Visual Studio to Unity, and it might catch some crashes. You can also check the log files, and load up dmp files in Visual Studio, to investigate the issue.
If you're having a lot of Editor crashes, I'd stop using play mode in the Editor. Test exclusively in builds, until you've resolved all your crash issues. You asked why it doesn't run like in Visual Studio, well that's how Visual Studio does it.