My take on this is yes and no. It’s entirely up to you.
I’d love to tell you to forgo the normal tape and only use washi tape or vice versa. But as with many other things in life, different things have their purpose and function.
Sometimes I use the general masking tape to cover certain spots that prettiness is not required. Plus, the general ones have a stronger glue and can stick better wherever you want it to, for instance, the double-sided tape mentioned in this article. However, I had a problem removing the residue, as the adhesive tape was too strong.
Sometimes I use washi tapes on the wall, tables, journals, books, cabinets, paper, etc. This kind of tape is low-tack adhesive. Just tear and stick.
To sum up, both the tapes have different functions and ways of using them. If you only need it for everyday use or cover the hole, usual adhesive tape can do just fine.
However, if you want something to make things prettier or beautify the white wall or blank planner, then washi tape is the answer.