No, you do not always need a dedicated WordPress Hosting Plan. The choice depends on what you need for your website and how it was built.
If you are using a pre-made template with many plugins, WordPress Hosting could be a good idea. But if your website is custom-made with good security and backup systems, you should not have any problems.
We manage many WordPress sites using shared hosting, with great results. These plans often give us better speed and more options to customize. So, you do not always need a special WordPress hosting plan - it all depends on what your website needs. Moreover, it is too expensive for the actual use for most companies.