Scrolling was an important aspect in the evolution of shmups.
During the sort of "second wave" of arcade shmups there was a lot of experiments and gimmicks looked into as a way to keep the genre fresh, and I feel like scrolling won out as the direction of travel pretty quickly, certainly 1984 at the absolute latest, when games like Xevious (released end of 1983), 1942, and Star Force reigned in the shmup world.
But really, I'd argue it had already started around 1982 when games like Time Pilot, and Moon Patrol were about, as well as 2600 games like River Raid, its port of Vanguard, Empire Strikes Back (which inexplicably became quite popular here in Britain via its C64 clone "Attack of the Mutant Camels") as well as its well respected clone of Defender "Chopper Command" etc etc. One of the biggest shmups on Spectrum was a clone of Konami's 1981 arcade game Scramble called "Penetrator"
Unlike with platformers, A lot of these shmups simply aren't possible with flick-screen progression, you need to constantly see ahead.

