My two cents as a user: I am strongly opposed to this suggestion. The good website design arguments proposed in the first post are totally consumer / content consumption oriented.
Manager is not a “website” but an accounting program. Gmail, Google Drive and many many other powerful applications do not follow the supposed “good website design” as outlined in the first post. Manager is used to get things done with lots of input/output as opposed to the browsing/reading/consuming which is done on a regular consumer facing website.
Since this suggestion is entirely based on taste and opinion, I will share mine. If it ain’t broke, don’t fix it. Learn to use manager.io as you learn to use any other powerful application. The dumbing down of UX is about making consumers feel familiar with an interface and lower abandonment. Manager does not have an abandonment issue because it is not consumer oriented. As such, the program needs to be learned and can then be used easily and seamlessly. The tabs have never bothered me and I am very fast with using manager and always find the tab I want without having to drill down in menus. Also, the tabs can be collapsed which moves them out of the way for more screen real estate.
An app like manager is about rapid input/output and switching, so hiding tabs would just add time to the workflow for no other use than looking “clean”. I rather use an efficient product that I have learned than a clean but less powerful product that is easy to use out of the box. My suggestion, learn manager and get used to its navigation and you will soon forget the tabs even exist.