For the game’s “slowness”, I’d say the issue lies in the enemies:
- They’re somewhat tanky (long time-to-kill per enemy, even on smaller-looking enemies)
- There is a lot of downtime between enemy waves
- Most enemy types becomes stiff as a rock as soon as they get in position (only exception I can think of are the ghost enemies that fly from one side of the screen to the other), making them feel very static as a result
So if these issues were addressed I believe the game would feel faster.
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As for the need for a scoring system, they add depth beyond “just shooting and dodging” and beyond just playing safe/turtling the whole game, add longevity/replay value, and adds a gauge of player skill to a shmup beyond “how many lives did I end the game with / did I beat it without continuing?”. A scoring system often incentivizes players to play in a certain way, such as asking them to take risks by having decidedly “active” playstyles like chaining kills together, collect items before they drop off the screen, or killing enemies with special weapons. This especially is the case if the player can earn extra lives by scoring, encouraging them to play by the game’s rules to that can be rewarded.
Certain shmups have incentives for letting off the trigger (not necessarily for scoring reasons), such as charging up bombs, gathering items, or delaying kills to set up for chaining consecutive kills for a combo if the game asks for that kind of behavior (which would be a scoring reason).