OP, I think you will struggle to unpick reasons behind ICs student satisfaction as there are so many potential variables.
London generally has lower satisfaction rates, with Borojo's DD being a clear example of someone who would have been happier elsewhere. DS knows several others. IC has more money, and generally better facilities, better accommodation and indeed better courses (certainly if you look at the bottom end of the education offer in London) and so tends to have better satisfaction rates than other London Universities, but these will still be lower than elsewhere in the country. But even so 50% or more are happy with the course/London/etc. The regular MN debate is essentially about whether London should be avoided because a larger proportion of students are unhappy, when the same environment clearly suits others, who go on to do very well.
University financing can be a bit of a surprise. I went to a alumni talk about three years ago given by the former LSE Director. Only about 10% of their funding comes from the Government. Fees from UK students does not cover the cost of educating UK students. Teaching lab subjects is far more expensive than teaching classroom subjects the same will be even more true at IC. The gap will be made up from research income, overseas student fees and more. IC, UCL and LSE live or die by their international reputations so maintaining these are crucial. There is always a question of how much UGs benefit from being at a research orientated University. If you are really interested in your subject being in a research orientated environment it will probably be fun. If you want more support and hand-holding, perhaps not.
You might instead be better off better to focusing on the question in the original post, which is about which teaching methods different Universities use and what will be best for your DD.
Having post grads teach classes, and I suspect, based on DS' parallel experience, many will be post-Doc not PhD students, is pretty standard in top American Universities. Oxbridge seems to be the anomaly. DS, like Purple's son, finds academics accessible and supportive via office hours and email. Indeed sufficiently for us to concerned at their workload, though the explanation seems to be that only a small proportion of students take advantage. I assume a physics course will be more structured. Economics at the LSE allows for a wide range of third year options so classes will be smaller depending on the popularity of the course. DS experience has been that larger groups are not a problem as fellow students don't say much in class. And that further help, if needed, can be found outside class. I am astonished at how many of the junior staff who taught me many many years ago at LSE have gone to become seriously big names. PhD and post-doc students at IC are equally likely to be very able and ambitious.
Maths at University, and much of DS' degree is maths and I assume this will be true for physics, seems to be different from at school. At school maths was the subject that involved the least work. Teachers would aim to have everyone understanding the concept before they left the classroom, and then it would be a case of (carelessly) dashing through the homework. At University DS is told to spend two hours preparing for a lecture so he is familiar with the material, and will then spend several hours after making sure he is on top of the content. Concepts are progressive so you need stay on top of it. Having A*s at A level does not seem to be a perfect predictor of who will thrive, especially given how directed some secondary school education systems are.
This then leads to a question about whether the hard work required is getting you further or is simply, as seems to have been suggested upthread, to make up for poor teaching. DS and his peers have been surprised at how relativity light the workload for STEM subjects is at some Universities outside the Oxbridge/London triangle, with one or two complaints about lack of stretching. Similarly DS was helping an able friend from another University who wanted to apply to LSE for a Masters, only to discover that the boy had not covered nearly enough of the technical ground. But that is random anecdote. I don't know how equal degrees are from different institutions. What is certain is that IC degrees are normally held in high regard by employers and other Universities both in the UK and abroad.
So back to why your DD wants to go to University. If she loves her subject and she is happy to put the work in, and is not fazed by living in London, she should love IC