In a way it does help me focus more on the bullets and less on the unique mechanics but sometimes that mechanic makes it more fun. I liked the graze factor of SA yet loathed but found the UFO mechanic intriguing (sorry Drake).
And sometimes the mechanic is what encourages you to dodge the bullets and makes it more fun, rather than just taking an easier path

I couldn't agree more. My biggest complaints with UFO and TD is that theres a chance (higher later on) that you lose a life trying to get a life. (I'm bad, I know) Just being able to focus on the game and gaining life through the points items that fall towards you or by scoring is the least rage inducing for me.
I'm a bit confused why you noted 10D here, but the way I'm reading this is "I don't want to have to do anything special in order to get extra lives". While score-based extends are great since ideally they should push you to actively work with the game's mechanics for survival, EoSD and MoF both fall utterly flat in this regard by handing every player all the extends before the end of the game regardless of how good they are with the mechanics. In the same light, PCB's distribution of the extends makes it so that every player will get five, and probably six or more, not doing anything in particular for them at all.
It's like because of this, you've internalized that the game is supposed to hand you a certain amount of lives by the end of the game. Sure, ideally, you're going to get the maximum amount of lives you find feasible, but if actively getting one extend is hard for you to get or you think you might die trying, there's always the option of y'know not getting it and just staying where you are. You haven't lost anything but your opportunity. This is what extends are; a reward for fulfilling some requirement. They aren't lives that are tacked onto your starting total but just happen to show up later in the game. Well, I guess they are for the games mentioned, but the point is that they shouldn't be.
What if MoF did this and only the first extend was really easy, and then rest were say 400m and up from there? Would you be more incentivized to score?
Actually a return of SAs grazing system would be welcome. It was simple enough, but somewhat more intriguing than MoF. And MoF was a little too hectic with the score bonus getting reduced the moment you wouldn't gather pickups or shoot fairies. That had a greatly demotivating effect on me.
SA's graze system I have two main disagreements with, which are the lack of focus on the POC and the milkiness of quantity-grazing for score.
With all items flying towards you at max value for some grazing, which most of the patterns are centered around, it removes the necessity to move up to the POC to collect, when POC itself is a magnificent thing. What this does is basically let the player be content sitting around idly grazing fixed or aimed things (not that this is very true for high scoring) around the bottom of the screen, which the POC itself is directly against. I find it interesting how you say UFO pins you at the bottom yet don't notice this, while I'll argue it's the exact opposite. Now as said SA's patterns are designed to work with this, so the POC is sometimes infeasible to reach, like often in stage 4. So it isn't a huge deal in execution, but I don't like it on principle.
Second, the system ends up early that you milk patterns for graze. That's just bad. Especially with ReimuA. Like I said before, the latter-half's focus on survival while getting faith and more graze is great, but... it's a graze milking system nonetheless. I'm very hard-pressed to name a game where your quantity of graze is important for scoring and it somehow doesn't run down to milking things. Me and others have thought long and hard about how to frame a game's mechanics around the "quality" of grazing, or how long you were grazing things intensely and how often you shoved yourself into danger, rather than having patterns yielding huge graze points and skewing distribution. This, I think, is a much better way to encapsulate the main point of grazing, which is to have the player force themselves into danger in order to be rewarded. However, I haven't yet been satisfied with anything I've come up with as a coherent system either (after scrutiny), so bleh.
Then I'll poke a little. UFO felt more restricting and had you pinned more at the bottom of the screem because moving would often mean collecting the wrong UFO.
I'm... not actually sure what you mean by this. How does the conflict of more than one UFO on screen force you to the bottom? That just avoids all of the UFOs. To begin with, the UFO system is what gives the player the incentive to start moving all over the screen where they might not normally want to go due to bullets. When you give the player this opportunity, it creates the risk-reward scenario of offering the player extra resources or points for daring but successful behaviour. But even with like 4 blinking UFOs on screen somehow it's usually the bullets that prevent you from getting the UFO you want (i.e. stage 4), so I'm not sure why the UFO collection is why you'd say it has you pinned.
EDIT: Ammy's right, if someone wants to take this then make a new thread lol