The answer here is certainly no. Many dwarf galaxies (e.g. the Magellanic Clouds) don't contain supermassive black holes, although some may contain less massive intermediate-mass black holes (Mezcua et al. 2018). As they are the most numerous type of galaxy in the universe, it's quite possible that most galaxies, in fact, do not contain supermassive black holes. This shouldn't be too surprising; if the bottom-up theories of supermassive black hole formation are correct, many intermediate-mass black holes must coalesce to form a massive one. Dwarf galaxies simply wouldn't have (or be able to form) the requisite population, in most cases.
That said, a number of dwarf galaxies have been observed to host supermassive black holes (notably including M60-UCD1 and Hen 2-10, among others). These have provided, and continue to provide, insights into the formation and evolution of low-mass galaxies.
Some users here have also identified some massive galaxies without supermassive black holes, including M33 and A2261-BCG. The former has a bulge, but the central stellar velocity dispersion is low, implying there is no black hole at its core (Merritt et al. 2001), assuming the required parameters are known well enough. In A2261-BCG, it's possible that one or more central supermassive black holes were ejected, leaving a "puffy" core without a black hole. Keep in mind, of course, that this is only one possible explanation for the observed distribution of stars in A2261-BCG.
In general, a central supermassive black hole does not influence the large-scale kinematics of stars and gas within a galaxy. Most supermassive black holes are much less massive than their host galaxy; I believe Sag A*, at the center of the Milky Way, is on the order of about 0.001% of the total mass of the galaxy. Even massive ellipticals like NGC 4889 have black holes about 0.1% of their total mass. As far as I know, ultra-compact dwarfs have the highest black-hole-to-galaxy mass ratios, with an extreme example being the previously-mentioned M60-UCD1.