No, you should not use concealers all over your face because concealers are mainly used for spot coverage to help you hide hard-to-cover skin imperfections.
There are a few reasons why using concealers all over your face is not a good idea:
1. Consistency - Concealers have a thicker consistency than foundation and when applied all over your face, they will make your skin feel cakey and thick. This is not a great feeling especially if you're planning it wear your makeup all day.
2. Price - Concealers come in smaller bottles and are more expensive per volume when compared to foundation. Using concealers all over the face is simply not economical and will hurt your wallet over time.
3. Shade Options - There are fewer shades to choose from. Shaded concealers are commonly used under foundation with a similar shade. Since your concealer will NOT do the main job of matching your skin tone,  companies don't create many different shades of them.
This means that you will most likely need to mix concealers of different shades together in order to create a shade that matches your skin tone if you want to apply concealer all over your face.