I am convinced that there's a (paid!) market for this, but you are also asking for feedback from the wrong crowd, that's why you are getting feedback like this
> There's zero chance I'd ever sign up for such a service.
Majority of HN users are I am guessing under 50 and most if not all have good paying jobs -- money is a factor in quite a few instances of loneliness directly or indirectly. Ex: Guy loses job, girlfriend leaves him, starts drinking and become lonely.
The loneliness epidemic is also very prevalent in the 50+ age group, esp. with rising longevity and healthcare facilities in the developed world, people are living longer and longer.
I saw in the news the other day how the mailman was sitting and reading mails to senior citizens in some french village and they were paying him for it.
You should do a quick and simple MVP, and position it positively, like "make friends anywhere in the world" or something like that, not too cheezy, but nothing "negative" sounding like "overcome your loneliness" etc cos that will just remind people how lonely they are.
I recently interviewed at https://www.keen.com and when I visited their site, it looked scammy like 1 of those online horoscope, lover gurus and tarot card readers. On site I learned that they are very highly profitable since 2004. It's a bunch of online properties where people call into a phone # and discuss their relationship, get "happiness advice" etc. Apparently quite a few of those "Advise providers" are making a fulltime income.
You could apply the same principles to penpal / email to help people combat loneliness, make news friends, and get relationship (this also causes loneliness with breakups, divorce etc) advise etc.
Email me if you wanna discuss more. Email in bio.