Imagine a time before instant communications, where you have no idea how life has treated the recipient since you last saw them and it might take months for your letter to arrive. It is a sincere hope that they are well and that tradgedy has not befallen them.
It would be neurotic and unreasonable if your last update on their life was only days or even hours before, but in the days of letters hope is really all you had. It's just honest.
I have used a check. I'm more likely to be able to get a mortgage and buy a house than to be accepted for a rental again, though I'll likely die before paying it off. I still keep a fair amount of actual cash at home "just in case".
Will be interested to hear your guesses.