Do all publishing companies require that you have a publicist to publish your book?

No. Advertising and marketing the book, as well as proposing public appearances by the author is the responsibility of the publisher. It is, however, a good idea to have an agent you can trust to handle the bureaucratic side of things -- negotiating appearances, fees, etc. -- so that you can focus on writing and the appearances themselves. There's a lot more work that people realize that goes into planning and dealing with the business side of writing, and it's easy to get lost in it or have it consume all (or near enough that it feels like it) of your time and energy.Do all publishing companies require that you have a publicist to publish your book?
Commercial publishers (the kind you see in bookstores and libraries) will do the work of promoting your book, to back the investment they are making in your book. Self-publishers do not require nor provide a publicist, leaving all of the work in your hands.