I can only answer this with regard to my own use of email as a "letter-writing" platform and that of my family and friends who communicate with me via email.
It is so easy and convenient to sit at the computer keyboard and type a message--long or short (mine are often longer than any letter I would write on paper to mail). Because I don't have to hold a pen in my arthritic hands and form my nearly illegible handwriting, find an envelope and stamp, and then mail my message, I communicate much more frequently (and, as I mentioned, at length) with family and friends who live in other places than I ever did before the advent of email.
Yes, I'm old enough to remember B.E., "before email", more than 30 years ago. I even remember B.I., "before Internet." In those days, one had no option but to use paper and pen for writing letters or else call a person on the phone. Consequently, written correspondence was much more limited than it is today, and--since those were also the days of toll charges for long-distance phone calls--most people didn't talk to distant relatives and friends as often.
I often prefer emailing someone rather than phoning them because it's faster. I get the reply and usually answer it, so a back-and-forth conversation ensues. I like email! Because it's such a handy medium for communication, I use it a lot. In that respect, I write more and so do my correspondents.
Whether an individual person's writing skills are strengthened or weakened by using email depends entirely on his or her determination to write grammatically and structurally well in the email medium. Not everyone cares enough to do so. I do not text or send instant messages because they tend to be carelessly dashed off full of abbreviations--some nearly impossible to understand--in a nonsensical type of personal shorthand. I don't send them, and I don't want to receive them, thank you very much. I do believe that texting is weakening the writing skills of everyone who uses the method frequently, especially young people who have been doing it most of their lives. It is especially ruining the ability to spell.
I also don't "do" Facebook or Twitter because I don't care to write every thought I have in short bursts, nor do I care to read much of what is posted on social networks. Unfortunately, some people who previously wrote to me via email only write on Facebook and/or Twitter these days, so I've lost some correspondents to social media. It is what it is.