I have a close friend who met her husband on Match. They've been married almost 20 years so I guess anything is possible. As for my own experience, Match was the site I met the most women. Virtually all of them were VERY serious about finding a long-term relationships. At the time, so was I. Never tried e-harmony.
Conversely, you're right about Tinder, definitely a place to get laid - whether you're single or married.
I tried POF many, many years ago when it was simpler format. I was probably around 45-50 years old at the time. I believe I had only a half-dozen dates, none of which went beyond a second date. Maybe it's changed, but after a while I felt the women I was encountering enjoyed chatting online more than actually meeting in person.
At the end of the day, I think you're right: go to a store, market, library, etc, and strike up a conversation. Plus, the lighting is good so no unpleasant surprises later!