There's only ever been one good Stagecoach livery imho, stripes. All others are ordinary at best, downright awful at worst. Which somehow makes stripes even better.
Strong and bold, and like all good things, it divided opinion at the time, even horrifying some traditionalists. It wiped away several much loved liveries, and Busways notably even negotiated a temporary stay. I loved the Busways scheme, but even I would pause if offered a return to stripes or yellow.
The scheme has absolutely stood the test of time, would still look good on today's buses, and looks superb in preservation. You can't conceive of the UK bus scene without it now.
The obvious benefit was obvious, projecting the corporate brand, a basic and obvious marketing tool. It's a sign of its superiority that it worked in that role both when Stagecoach were a small independent trying to crack different markets with various unique selling points, but also later when they were notable for being the dominant incumbent.
I never really knew what the logo meant, but that was part of the charm - this bold new livery sweeping away the old guard was something so modern it was beyond our comprehension. The small but discrete use of a tagline was a nice nod to localism, and unlike other liveries, was presumably not much of a hassle when it came to moving buses around the country.
Given it works on basically any bus or coach model, from a VR to an RH, a Dart to a Premier, a Routemaster to a Lance, and more importantly looks good on all of them, is a good reason to perhaps consider it the best (corporate) bus livery ever invented.
I love it so much, it forms a large part of my 1:72 scale model collection, and I am able to deploy a whole fleet of them. When turned out, they get pride of place, the middle eye-level shelf.