As already said it doesn't work like that. Simply put you need to do your job and that is to add constraints and solver needs to do its job and that is to calculate correctly if added constraints suffice to get fully constrained sketch.Even without adding tangent constraints to the 2nd drawing, as soon as you add a vertical or horizontal constraint the sketch
has only one solution, thus zero degrees of freedom. That said, I can see why the solver might not recognize it.
In your example solver did the job correctly it informed you 1DOF still exist and multiple (constraint) solutions to solve that are possible. Adding tangent constraint to remove that remaining 1DOF is not the only option. Use different set of constraints and you will quickly notice sketcher is correct in both cases.