Why are binary signals drawn continuous in time despite being a digital signal
You are right and wrong!

If you would like to treat a binary signal as a discrete-time sequence having values of $0$s and $1$s, then you would plot them as all other discrete-time sequences, using the lollipop display.

However, for those electronic circuits that implement binary logic operators using physical devices (gates etc.), the associated voltage and current waveforms are analog in nature. What's binary there is the information that the voltage or current waveform carries. But the physical existance is analog. So if you want to plot them, then you would do it just like a logic analyser (oscilloscope) would draw them on their phosphorus crt screen...