Can you make a game with Unity assets?
The simple answer is yes, the more detailed answer would definitely be yes. you can make a complete unity game with unity assets which you can find on unity asset Store.
you can also make a game using only the free unity assets. You do not even have to use paid unity assets but you can also use them.
One example I can give you is, The Last Tree, the full game was made using assets from the Unity Asset Store. Here the developer explains how he made the complete game with the help of Assets from Unity Asset Store.
https://youtu.be/g5f7yixtQPc .
No Time, No Budget, No Problem. Finishing The Last Tree.
Can you make a game with only free assets:
Yes you can, in unity asset store you can find a lot of paid assets that have free version is well so in the free version there is not a lot of content but if you just want to get started you can easily use the free Assets and if and see if it goes with your game, the look and feel then you can like go and purchase the paid asset but you can also freely use the free asset and make your game.
It's up to your imagination you can easily customize the asset, add details to the Asset so definitely you can easily make a game that has been created using only the free assets from the unity asset Store.
If Everyone is using Assets from Unity Asset Store, Would Every Game not Look the Same:
So if we look at this example you can easily create a game using as it is from Unity asset store and sell a million copies. Now the question is how you can make your game look different. If everyone that starts using Unity assets from the Asset store then would every game not look the same.
So so the question is how to make your game look different even if you are using the unity assets and in the talk (please listen to the talk) He explains his how he, you know… nit pics and changes a few aspects of the asset so as to give completely custom look his game so that he is game would not look lifeless.
Should you use Unity Asset Store
Now the final question is should you do it. The answer depends on where you stand. If you are totally new to game development, making each and every asset from scratch would be a tiresome job. It's really hard to make each and every asset manually and to get a final sketch of how your game looks.
It would take months just to get a prototype of the game but using Unity Asset Store will head start your game development by months if not years.
It will really help you to get the product and then decide whether you want to continue with this project or not.
If you would start creating each and every 3D model from scratch and then go on thinking that I don't think this game is worth it, I don't think I am going to proceed with the project. So all the work and time that you spend on creating 3d models manually would be a waste of time. so definitely use Unity asset store wherever you can to save your work.
If you are a team then definitely make your own assets because you will reuse them in a lot of different projects but if you are a developer and you want to learn and you want to create your portfolio definitely.
Conclusion:
There is no shame in using Unity Asset Store. Dumping assets from the asset store will not give life to your game, You will give life to your game by using your imagination and creativity. The assets will just help to visualise what could otherwise take months if you did everything manually. Use Unity Asset Store and add to the assets and customize everything according to your need and the feel of your game. And also listen to the talk, you will learn a lot