agree partly with your first picture of asus4 but if you leave the d string open your double the D as opposed to the E of A,E, and D............Sus4 (or just sus) stands for „suspended 4th“. The 3rd of a major or a minor chord is suspended and replaced by a perfect 4th. A major chord has the tones A (1), C# (3) and E (5), ... a Asus4 chord has the tones A (1), D (4) and E (5)

so i'll stick with just lifting a finger!