I mean, it seems to me that to “build an intuitive understanding” you need to use calculus or at least algebra, so you can model the circuit components mathematically in the time domain and the frequency domain.
As someone who did the math after gaining an intuitive understanding of circuits, I still tend to design circuits by intuition first and do the math after.
Imagine something like: "This needs to be biased a little bit more positive, here we use a precision diode, that needs a little bit of negative feedback, ..."
Math is important, but much more important (IMO) is a systemic understanding of how parts of the ciecuit influence each other and where they are (or should be) decoupled more or less.
