Is it OK? I'm genuinely not sure. I have been considering a new year's resolution not to keep propping up relationship that aren't reciprocated. Are they "not initiators" in all relationships, or just with you? Why do you conclude that it's ok (genuinely interested)?
It's entirely natural that some people become "initiators" as a relationship develops. At the beginning of a relationship, person A will initiate X% of the time, and person B will initiate (100-X)% of the time. Unless X is exactly 50 (unlikely), this means one person will naturally initiate more than the other. And then, over time, the person who initiates less will realize that the other person tends to initiate, and will come to expect it.
Notably, that doesn't mean that the person who initiates less doesn't value your company! (Of course, it also doesn't mean that they do value you, only that the frequency of initiation is not a good proxy for the health of the relationship.)
I'm with you. What I realized is when you take the lead and throw a party or happy hour at a bar or something, your social status increases as well. Most people are followers, few are leaders. If you feel lonely because you don't get invited to parties or events, it might be that they don't think of you as a fellow-follower. It could be that you're actually the leader type and could benefit from that.
I am one of those people that could be described as "not intiators". I genuinely appreciate when people get in touch. I am sorry that I'm almost never the intiator, it's a trait I unfortunately have and I'm working on getting better.