Well when you have a chord progression like A7 D7 E7, you are changing the key on every chord. A7 is not in the key of A major, it's in the key of D. If you learn the modes, you will then understand that it's much easier to just play the A mixolydian scale over an A7 chord. The mixolydian mode is the scale to use over the dominant chord since it's the 5th mode of a major scale. The dominant 7 chord is the 5th note in a major scale. See how they are equal.

Now when it comes to blues, the blues minor scale is used instead of the mixolydian mode. So A minor blues scale is played over an A7 chord and so on. The A minor blues scale can be used over the entire progression of A7 D7 E7 and still sound fine. The only problem in my experience is that the solo then becomes "boxed in". You are limited to using only 6 notes for an entire solo. Expanding to using a different root scale over each chord opens up many more possibilities. The key behind this thinking is understanding what notes are in each chord. So as you play over an A7 chord, you know that the chord is made up of the notes A, C#, E, and G. So when you play these notes over an A7 chord, they will sound consonant. Every other note will sound dissonant. Musical melody is a constant balance of dissonance and consonance. You can't have all consonant notes because then the music will sound boring and predictable. Dissonance is what gives the music personality. The b5 or Eb in the case of an A7 chord is an example of dissonance, or better yet the dissonance associated with the "blues" sound.

So when you jamming over chords, think of what notes are in each chord as you solo over each. Those are your goal notes. Throughout your solo over a chord, you goal is to eventually get to one of the notes in that chord. If it's the chord progression A7 D7 E7, use the A minor pent as a guideline.