I have tried this, (even with fairly distant extended family,) and in some cases, I have never heard from - or seen - them again. Obviously weren't that bothered about me were they?
I do miss a couple of them, but did get sick of ALWAYS being the one to contact them, and of them making zero effort with me (even forgetting my birthday, and my DH's and kids birthdays,) quite often.
I currently have a small issue with a very old friend who never, ever, ever contacts me, and it's always me who texts her first. I do wonder if I stopped contacting her, if I would ever see her again! 
Thing is, I do like her a lot, we go back many years, and she always remembers birthdays, and buys lovely gifts at Christmas etc (I do for her too,) and she does message me with big news - like her brother dying so I could attend the funeral, and an old school mate of ours dying too.
But it grates on me a BIT that she never texts me to see if I want to meet for coffee, and it's always me who does it.
Thing is, I don't want to not see her again, as we get on well, and have lots of giggles when we meet. We also have lots in common, and lots of happy memories from the last 30-odd years. I know her family members too, and see them every so often in passing.
So I guess in answer to the OP, it depends how much you like the person in question, and if you want them out of your life, or want them to stay in it. If them never really contacting you, and you always having to be the one to do it, is the only issue, then I would suck it up and just text them if you don't hear from them.