Question Download Apps from Play store automatically

Not sure where I should place this question.

So in the past week I've had my phone replaced 4 times, and possibly a 5th. Its a long story.
And I've noticed how time consuming it is to re-download every app.

I was just wondering is there an app that you have a set list of apps that will automatically be downloaded from the play store?
Lets say every phone regardless of what make or model you use apps a,b,c,d.

And the play store never downloads them automatically.
My question is simple, is there a way to have a set predetermined list with in an app, in which the play store will download them.

This is coming form a non-rooted phone.
I've also have had issues with titanium plus on rooted phone.