The cover letter would be only good if you want to prepare a more professional looking home application. Other than that I don't think it will be necessary. What matters most is you financial ability.
Yes, and a lot of people have the same financial ability as you say but sometimes a nice accompanying letter will do the trick to stand out in the crowd.
I depends how many applicant there is. When I first came, everyone said one flat receives 500 or even 100 applicants.
But in my case, where there is no applicants to my flat among the crowd of visitors, maybe the immobilen company should rather use a cover letter to attract applicants
I saw that you are looking for 4+ rooms for about Fr. 2000.--, that is what everybody is looking for - that price is even too low for the market most of the time
At the time I was looking as small as 2 pieces for 1500.- CHF. Is that unreaslistic? I found a lot of renting offers within this range. Were they fake?
So what is your suggestion to form a realistic expectation about what I can rent?
I also find that notice boards of Hospitals (CHUV), Ecole Hôtelière, University or any such schools, are a good source to find apartments which often haven't been too advertised