In simple words, No! Mastering a design tool is a must for web designing, but it shouldn’t necessarily be Photoshop. Some might argue it should be completely avoided when it comes to web designing because of some clear demerits -
The domain of creativity in Photoshop is huge, but that of execution on the web is constrained. So, it's easy to let go of the limitations of the web and create designs that might be tough, or even impossible to construct using HTML. This might hamper your design workflow.
Photoshop works with pixels, but the web prefers scalable design with vector graphics.
Photoshop doesn’t help much with interactions like button clicks or mouse hovers while building mock-ups.
Photoshop makes it tedious to create responsive designs, which is a must for websites.
Having said these, there are more popular and efficient alternatives to Photoshop, like Figma, Sketch, Adobe XD and InDesign, etc.