Thank you for raising these questions about the Sensei’s Library article.
Concerning the first diagram, you’re right that the ripped keima shape is considered bad for Black because Black’s stones aren’t connected. White’s stones, on the other hand, are connected, which denies Black a good attack while the local balance of power is so unfavorable.
In the second sequence, you mention that White has no base yet. This is true, and it’s an important observation. But here, Black can’t get a good attack because of a weakness at q14 (White q15 would secure the group and cause Black problems). And even after Black defends at q14, White still has options. For example, White can escape toward the center, either down or left, and may even have a counterattack at h17. White could also counterplay by attaching at l16 if no better options are available. Having all these options makes White safe despite having no base.
Concerning the third diagram, you mention that the space is narrow for White, but it still separates Black’s stones. This is true, but Black is also a lot more powerful here than in the previous sequence. Black’s defense at 4 (q14 in the previous diagram) is already in place, to name the most important factor.
In general, when considering both the long-term implications of a move and the current state of the board, you can’t ignore the concept of power. After all, lacking a base doesn’t mean a lot if your opponent is too weak to launch an attack.
One of the bad things about the ripped keima is the ripped stones only have 3 liberties so are weak. N16 only has 3 liberties, whereas marked stone in second diagram has 4. This makes a big difference to the local efficiency, and the ripped keima is bad is about local shape. You are right that thinking more globally it’s still possible for the player ripping the keima to be weak, though that’s not really the case in example yet. The important thing not mentioned is the ripped keima only came about because of black’s exchange of 4 for 5 which is bad, black should just jump on right side or hane under 1: then black has all the goodness of white not having a base yet you identified, with none of the ripped keima bad local shape.
But also this isn’t the best example of ripped keima, but author was probably trying to make one with few stones. The prototypical beginner broken keima is one where they ALLOW the opponent to rip through a keima where both stones are important which was not previously separated, whereas this example black is just playing some stupid exchange not changing the topology of the groups. Here is such an example from the first beginner games I clicked on in progress: 24 is terrible because 25 rips through the keima Mag_05 vs. avirasy
This is always an important consideration. But note that after 1-2-3, White already doesn’t have a base. The additional exchange 4-5 creates the ripped keima shape, and it does not remove White’s base (since there already was no base). White was weak before 4-5, and White is still weak after 4-5, so the question is: is White stronger or weaker after 4-5 than before?
After 1-2-3, the loose shape of White gives Black several options. For instance, Black can play at M17 to make sure that White doesn’t make a base; Black can play hane at O18 (possibly to connect two Black groups by underneath); and perhaps in the future, Black might be interested in cutting by playing at O16. All in all, the two White stones O17-O15 look pretty weak and short in liberties, whereas the two Black stones Q16 and P17 look pretty strong.
After 4-5, the hane at O18 doesn’t work as well as before, the two black stones P17 and Q16 look weaker than before, and the black stone N16 looks pretty weak too. White still doesn’t have a base, but now White can play at Q15, or at R17, or at M16, or at M15, and all those new possibilities can help White make life when needed. In particular, the Black stone at N16 is short in liberties and might get captured in the future, which might be an eye for White.
All in all, creating the ripped keima by playing the forcing exchange 4-5 strengthened the two White stones, weakened Black stone 2, and added a weak Black stone 4.
About comparing the two sequences, I suggest comparing with this diagram instead:
In both diagrams, the choice of whether to play 3 at O16 (nobi, second diagram) or O15 (tobi, first diagram) belongs to White. However, the choice of whether to create a ripped keima with 4 at N16, instead of a classic corner extension at Q14, belongs to Black. Most likely creating the ripped keima is bad.
In this image, two stones at the center have 4 ‘hot’ spots marked with x. It’s better for both players to avoid these spots. Because putting black stones there will be inefficient and white stones will be weak. This explains why empty triangle and ripped keima are bad shapes.
But sometimes bad moves considered by this principle are played as joseki, as shown in this image.
I explain this as such moves are played to settle the shape in sente to remove the possibility or flexibility of the opponent stones. So taking sente is also important.
sente + good shape = great
sente + bad shape or gote + good shape = even
gote + bad shape = bad
And in your question, black is playing sente + bad shape so other factors like other people mentioned should be considered.