No, uninstalling old drivers is not necessary, even when switching brands or GPU architecture, as Windows will see a new piece of hardware and treat it accordingly, rather than using the old driver to run the new hardware, unless of course the old driver contains support for the new hardware as well.
Windows treats GPU driver installation pretty much the same as any other piece of equipment, but due to how many common pieces of software such as web browsers and video players hook into the video software subsystem, it's easy to have a failure of video card driver updates, leading people to think that the installers are just not as well written for those. Uninstalling the branded, hardware specific drivers and forcing Windows to use it's generic drivers that don't support certain feature sets can alleviate problems in some cases, leading people again to believe the driver installer was the issue, when it could very well be extra software on their system that was conflicting with driver installation.
A case against wiping the old drivers would be if you have a lot of custom profiles for games you play. If you're upgrading cards from a compatible line of GPUs, you should be able to keep your custom game profiles for your graphics driver while just updating the driver. On the other hand, if you don't want to keep any custom settings, modern GPU drivers should present you with the option to perform clean installs as well, making pointless any uninstallation requirements within the same brand.
The only time I would strongly suggest uninstalling the old graphics driver first would be when switching brands between NVIDIA and AMD, and not because the first should evoke major issues in the second, but for the reason that there can be extra, unnecessary software that is installed as part of a graphics driver package, and there's no point keeping the old software around for a piece of hardware that's no longer attached to the system.