Your second example, without Komokus, is entirely different I'd say. Here I think

is a stylistic choice, though, I also think it tries to circumvent the underlying problems instead of facing it : D If you are unsure of how to handle frameworks then I would practice it and don't try everything possible to never have to face such situations.
Regarding the split with a 3*4-stone in place:
$$Bc Too good for White?
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 2 . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . 1 . . . |
$$ | . . 8 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 7 . . . . . . . . . . . . . . . . |
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$$ | . . 5 , . . . . . , . . . . . , . . . |
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$$ | . . 6 . . . . . . . . . . . . . . . . |
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$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
- Click Here To Show Diagram Code
[go]$$Bc Too good for White?
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 2 . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . 1 . . . |
$$ | . . 8 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 7 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 5 , . . . . . , . . . . . , . . . |
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$$ | . . 6 . . . . . . . . . . . . . . . . |
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$$ | . . . 4 . . . . . , . . . . . 3 . . . |
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$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
White played on both sides and when Black defends his group, he's also ending in Gote on the left.
$$Bc Feasible for Black?
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 2 . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . 1 . . . |
$$ | . . 7 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 8 . . . . . . . . . . . . . . . . |
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$$ | . . 5 , . . . . . , . . . . . , . . . |
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$$ | . . 6 . . . . . . . . . . . . . . . . |
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$$ | . . . 4 . . . . . , . . . . . 3 . . . |
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$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
- Click Here To Show Diagram Code
[go]$$Bc Feasible for Black?
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 2 . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . 1 . . . |
$$ | . . 7 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 8 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 5 , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 6 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 4 . . . . . , . . . . . 3 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
Black can also try to extend all the way to prevent White from taking the enclosure but then I think

is a very strong move and a fight will start in an area where White has more stones than Black. This is of course playable but personally I think White dictates the flow here.
Overall I can find multiple reasons why the white moves are good:

extends from the Hoshi stone and also attacks Black.

in the first diagramme takes a solid enclosure while also keeping up the pressure on Black.

in the second diagramme pincers and splits Black and so follows-up on
Black on the other hand:

in the first diagramme just makes a bases while inducing White to take his beloved enclosure.

in the second diagramme overextends and leaves behind weaknesses, so that it is unsure with what he will end with.
This is just my reasoning, though, and I am not stronger than you ; ) I also would like comments from stronger players.