Tl;dr: Few people genuinely want to do research internships at universities unless they are academically oriented. Successful students’ stories spread around. Juniors under pressure to land an internship emulate/copy templates. Despite sound advice from seniors, a lot of undergraduates send spam.
As an undergraduate senior currently studying at IIT Bombay, let me try to add to the already written answers by Aditya etc. with reference to my interaction with my seniors and peers. As has been mentioned in Aditya‘s answer, there are some formal channels to get internships; these are mostly helpful for top-ranking students, whereas the number of students wanting to do internships is much more.
At IIT Bombay, there is no mandatory internship requirement for graduation but I know other universities where this is the case.
As far as I understand, students, especially juniors (and to a lesser extent sophomores) are under quite some pressure to land a "summer internship" and the order of preference is typically as follows: Great company > Average company > Foreign University > Indian University > Current University ≫ Nothing.
For students who are interested in entering the job market after graduating, the order follows naturally, where the last few inequalities stems from peer pressure and the last one from “something is better than nothing”.
For academically-oriented students – primarily aiming to apply to grad schools abroad the next year – the first two options are not relevant. Here, the internship serves three purposes:
Doing decent/good work ensures a letter of recommendation for grad school from a Professor who is not from your current university (the general belief is that such a LOR is likely to be more helpful than a “local” one).
Research experience helpful for deciding fields of interest.
As somebody as already pointed out, free vacation in a foreign country.
Of course, the relative importance of each factor varies from individual to individual.
In the fall semester, there are often short sessions organized by student bodies on “tips on landing an internship” from successful seniors; I have attended a few of these. The common summary usually boils down to: if you are interested in some professor’s research write a short email with:
- short introduction;
- research you are interested in (after reading papers);
- previous research/study experience with linked/attached homepage/CV.
Although all our seniors strongly advise us against writing fake emails (like the ones you’ve mentioned) as it hurts the reputation of the student community and especially affects those who write sincerely, there are inevitably more than a few who feel desperate (because statistics of landing an internship via emailing are so low), skip over the “reading papers” bit and choose to send spam in bulk rather than a few well-thought emails. And inevitably, one “ideal” email gets shared which is copied and edited as a template. This leads to a “race to the bottom” as pointed out in the answer by Anonymous Mathematician.
Apart from the statistical factor, there is an obvious mental cost of writing a genuine email; posting spam takes little to no effort compared to writing a sincere email – I remember having written exactly one email which took me around two weeks including reading papers, references etc.
A short reply to Pete L. Clark’s comment:
If faculty members really wanted their students to do internships abroad, why aren’t they helping them out in some way?
Many students have little to no experience with undergraduate research and are looking to land an internship quickly. Professors do occasionally help students get such an internship abroad; this happens mostly in the case where the student has prior undergraduate research experience and is comfortable talking about the situation with the professor.