Lightvector's first diagram of a 4-4 that ignored a double approach, got surrounded at 5-5, and then lived at 3-3 raises an interesting question. Yes,
that particular way of living in the corner with 3-3 after being surrounded is bad for white, and the double kicks make it worse, but the more general strategic principle of a 4-4 allowing itself to be surrounded and living in the corner is
actually not so bad (as we used to think) and is one of the key lessons of AI fuseki. But if you do allow your corner to get surrounded like that, you should do
3 4 things:
1) get something sufficiently valuable from the tenukis, for example in my Leela Zero Opening Gospel video I look at the Kobayashi denied fuseki, and munching a 3-4 after an ignored press is well worth allowing your 4-4 to get surrounded, see
https://youtu.be/vupa_IM1wWY?t=521 2) live
efficiently later, which means play 1 kick and 1 knights move to 2nd line, or 2 knight moves, not 2 kicks (makes black too strong and still weakness inside), and not 3-3
3) live
at a good time later, not too early, not too late. If they play 5-5 and you immediately live in the corner in gote, it's probably a good exchange for them because they surround you in the corner (good topologically, making their 2 approach groups connected) and get sente for another big opening point, and that's better for them than if they took the big opening point and you got to play first in the double approached corner which not only gets your group out to the centre but separates their groups and gives them potentially weak groups. But it might not actually be so great for them depending what happens, maybe they would later wished to have taken the territory and base in the corner themselves. If living creates aims of cuts on the outside wall which doesn't have ample eyespace then it raises in priority. In general it might come a dozen moves later in the opening, it's still a pretty big opening move.
2 / 3 a) it's also ok to not live there and let the opponent spend
another move to kill it off whilst you do something else valuable, and even then you still have useful aji.
4) not make your previous stones sad (this is a general principle of efficiency), but in OP example as John points out the white top side pincer stone becomes weak when black surrounds the corner and gets strong (stay away from thickness/strength), so has become a liability, and would be better placed elsewhere.
Here's an example game of mine putting these ideas into practice. Note:
1) tick, I got nice wall press and then the sente turn
2) tick
3) faily-tick, though checking with a bot now it says it would have been good to have lived there even earlier
4) tick, no weak stones close to black's wall
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Fllecha
I'm OK with giving White 14 pts. in the corner. Either side can make a hane on the 1st line. Let's also give White 14 pts. for the stone on the top side, even though the bots tell us that that is an overestimate. So in the top left quadrant we estimate 40 pts. for Black and 28 pts. for White, a difference of 12 pts. in Black's favor. Each side has made 5 moves there. At this stage of the game the net result of 5 moves by each player should be zero. 
Since KataGo only gives Black a winrate difference of 20%, Black may only have made a gain of 5 pts. or less. But still, the play in the top left is a disaster for White.